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ICSE Board Problems , Trigonometrical Identities

Class 10: Trigonometry – Board Problems

trigonometry worksheet class 10 icse

Question 14: Evaluate without using trigonometric tables:

\displaystyle 2 (\frac{\tan 35^o}{\cot 55^o})^2 + (\frac{\cot 55^o}{\tan 35^o})^2 - 3 (\frac{\sec 40^o}{\mathrm{cosec} 50^o}) \hspace{1.0cm} [2011]

Question 16: Without using trigonometric tables, evaluate

\displaystyle \sin^2 34^o + \sin^2 56^o + 2 \tan 18^o \tan 72^o - \cot ^2 30^o \hspace{1.0cm} [2014]

Question 17: Prove the identity:

\displaystyle (\sin \theta + \cos \theta) (\tan \theta + \cot \theta) = \sec \theta + \mathrm{cosec} \theta \hspace{1.0cm} [2014]

Therefore LHS = RHS. Hence proved.

\text{Question 19: Evaluate: } \displaystyle \frac{3 \sin 72^o}{\cos 18^o}- \frac{\sec 32^o}{\mathrm{cosec} 58^o} \hspace{1.0cm} [2000]

Question 24: Without using trigonometric tables evaluate :

\displaystyle \frac{\sin 35^o \cos 55^o + \cos 35^o \sin 55^o}{\mathrm{cosec} ^2 10^o - \tan^2 80^o} \hspace{1.0cm} [2010]

Question 25: Without using trigonometric tables evaluate :

\displaystyle = \frac{1}{1} = 1

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13 thoughts on “ Class 10: Trigonometry – Board Problems ”

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The qustion no.2 Incorrect..

Thank you for pointing out. It was a typing mistake. I have corrected it.

It’s unable to understand the solution of question no.7

There was a typing mistake in the question… i have added one more line of explanation…. it should be easy to understand now.

I fixed it. Thank you for your contribution.

Technical issues from Q 12 Please sort them out

Let me check

Very helpful.

ques 9 has wrong answer

Good catch… it was a typo. We have corrected it.

(1-tanA)² + (1+tanA)² = 2sec²A LHS = (1-tanA)² + (1+tanA)² LHS = 1-2tanA+tan²A+1+2tanA+tan²A LHS = 2 + 2tan²A LHS = 2(1+tan²A) Here, we use formula (1+tan²A)=sec²A LHS = 2sec²A=RHS

By : MANGESH K REPAL

Sir, there are multiple ways of solving a problem. I have also included your way of solving the problem. Thanks

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Class 10 Maths Chapter 18 Trigonometry Important Questions

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In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, Chapter 2 may not specifically cover the topic of "Banking" as its primary focus. Instead, the curriculum typically includes topics related to commercial mathematics, which can encompass banking concepts. Commercial mathematics includes areas such as simple interest, compound interest, and profit and loss, which are essential aspects of banking and finance. Here are trigonometric identities class 10 ICSE important questions.

Introduction

What is trigonometry, class 10 trigonometry important questions and answers, icse class 10 maths chapter wise important questions, frequently asked questions.

In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, the chapter on "Trigonometry" is a fundamental topic that explores the relationships between angles and sides of right triangles. Trigonometry is a branch of mathematics that has wide-ranging applications, including in navigation, engineering, physics, and more. Here's an introduction to trigonometry in Class 10 ICSE mathematics: Importance of Trigonometry: Trigonometry is a critical branch of mathematics because it helps us solve real-world problems involving angles and distances. It's especially valuable in fields that require precise measurements and calculations. Common Trigonometric Formulas: Trigonometric Identities: These include the Pythagorean identities (sin^2θ + cos^2θ = 1) and various angle sum and difference identities. Special Angles: Trigonometry deals with special angles like 30 degrees, 45 degrees, and 60 degrees, which have well-defined trigonometric values.

Ans: Trigonometry is the study of the relationships between the angles and sides of triangles. It primarily focuses on right triangles, which have one angle equal to 90 degrees. Trigonometric functions and ratios, such as sine, cosine, and tangent, are used to establish these relationships. Key Concepts and Objectives: Trigonometric Ratios: The fundamental trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They relate the angles of a right triangle to the lengths of its sides. Right Triangles: Trigonometry primarily deals with right triangles, where one angle is 90 degrees. The side opposite the right angle is the hypotenuse, and the other two sides are the legs. Sine, Cosine, and Tangent: These trigonometric ratios are defined as follows: Sine (sin): Opposite side / Hypotenuse Cosine (cos): Adjacent side / Hypotenuse Tangent (tan): Opposite side / Adjacent side

trigonometry class 10 icse important questions

Q1. \(\frac{cos A}{1-sin A}\) - tan A =

(a) cos a (b) sec a (c) sin a (d) cosec a.

Explanation: \(\frac{cos A}{1- sin A}\) - tan A = \(\frac{cos A(1+sin A)}{1-sin A(1+ sin A)}\)- tan A =\(\frac{cos A(1+ sin A)}{(1+sin^2 A)}\)-tan A =\(\frac{cos A(1+ sin A)}{cos^2 A}\)- tan A =\(\frac{(1+sin A)}{cos A}\)-tan A =\(\frac{1}{cos A}\)+\(\frac{sin A}{cos A}\)- tan A

Q2. \(\frac{cos A}{1-sin A}\)-tan A=

(a) cos a (b) sec a (c) sin a (d) cosec a.

Ans . (b) Explanation: \(\frac{cos A}{1-sin A}\)-tan A = \(\frac{cos A(1+ sin A)}{(1- sin A)(1+ sin A)}\)- tan A =\(\frac{cos A(1+sin A)}{1+sin^2 A}\)- tan A =\(\frac{cos A(1+ sin A)}{cos ^2 A}\)- tan A =\(\frac{1+ sin A}{cos A}\)- tan A =\(\frac{1}{cos A}\)+\(\frac{sin A}{cos A}\)- tan A = sec A + tan A - tan A  = sec A.

Q3. Prove that : (i)\(\sqrt{\frac{1-cos\theta}{1+cos \theta}}\)= cosec θ - cos θ (ii) \(\sqrt{\frac{1+cos \theta}{1-cos \theta}}\)= sec θ - tan θ

Explanation: (i) L.H.S. =\(\sqrt{\frac{1-cos\theta}{1+cos\theta}×\frac{1-cos\theta}{1-cos\theta}}\) =\(\sqrt{\frac{(1-cos\theta)^2}{1+cos^2\theta}}\) =\(\frac{1-cos\theta}{\sqrt{1-cos^2\theta}}\) =\(\frac{1-cos\theta}{\sqrt{sin^2\theta}}\) =\(\frac{1-cos \theta}{sin \theta}\) =\(\frac{1}{sin \theta}-\frac{cos \theta}{sin \theta}\) = cosec θ – cot θ = R.H.S. Hence Proved. (ii)L.H.S.= \(\sqrt{\frac{1+sin \theta}{1-sin\theta}×\frac{1+sin \theta}{1+sin\theta}}\) =\(\sqrt{\frac{(1+sin\theta)^2}{1-sin^2\theta}}\) =\(\frac{1+sin\theta}{cos\theta}\)=\(\frac{1}{cos\theta}\)+\(\frac{sin\theta}{cos \theta}\) = sec θ + tan θ = R.H.S. Hence Proved

Q4. Prove that : sin 4 θ – cos 4 θ = sin 2 θ – cos 2 θ = 2 sin 2 θ – 1 = 1 – 2 cos 2 θ.

Explanation: Consider, sin 4 θ – cos 4 θ = (sin 2 θ) 2 – (cos 2 θ) 2 = (sin 2 θ – cos 2 θ)(sin 2 θ + cos 2 θ) [∵ (a – b)(a + b) = a 2 – b 2 ] = (sin 2 θ – cos 2 θ) × 1 [∵ sin 2 θ+ cos 2 θ= 1] = sin 2 θ – cos 2 θ = sin 2 θ – (1 – sin 2 θ) [∵cos 2 θ = 1 – sin 2 θ] = sin 2 θ – 1 + sin 2 θ = 2 sin 2 θ – 1 = 2(1 – cos 2 θ) – 1 [∵ sin 2 θ =1 – cos 2 θ] = 2 – 2 cos 2 θ – 1 = 1 – 2 cos 2 θ. Hence Proved.

Q5. The angle of elevation of a cloud from a point 200 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

Explanation: Let P be the point of observation and C, the position of cloud. CN perpendicular from C on the surface of the lake and C‘ be the reflection of the cloud in the lake so that

Trigonometry_Q5

CN = NC´ = x (say) Then, PM = 200 m ∴   AN = MP = 200 m CA = CN – AN = (x – 200) m C´A = NC´ + AN = (x + 200) m Let PA = y m Then, in right angled Δ  PAC, \(\frac{CA}{PA}\)= tan 30 ⟹ \(\frac{x+200}{y}\)=\(\sqrt{3}\) ⇒ x + 200 = \(\sqrt{3}\)y ⟹y = \(\frac{y+200}{\sqrt{3}}\) ...( ii ) From equations (i) and (ii), \(\frac{x+200}{y}\) =\(\sqrt{3}\)(x-200) ⇒        x +200 = 3( x –200) ⇒        x +200 = 3 x –600 ⇒        2 x = 800 ⇒        x = 400 m ‍ Hence, the height of the cloud = 400 m.

trigonometry class 10 icse important questions

The study of trigonometry in Class 10 ICSE mathematics is essential for understanding the relationships between angles and sides in right triangles. It equips students with tools to solve practical problems and lays the foundation for more advanced mathematics and scientific applications. If you seek additional practice and a deeper comprehension of the topics covered in the chapter, oswal.io offers an extensive array of class 10 Trigonometry important questions and answers to facilitate a more profound understanding of the concepts.

Q1 : What is trigonometry, and why is it important?

Ans: Trigonometry is the study of the relationships between angles and sides in triangles. It's important because it helps us solve real-world problems involving measurements, distances, and angles.

Q2: What are the primary trigonometric ratios?

Ans:  The primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

Q3 : What is the sine of an angle in a right triangle?

Ans: The sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Q4 : What is the cosine of an angle in a right triangle?

Ans: The cosine (cos) of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Q5 : How is the tangent of an angle calculated in a right triangle?

Ans: The tangent (tan) of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Chapter Wise  Important Questions for ICSE Board Class 10 Mathematics

trigonometry class 10 icse important questions

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Trigonometry Class 10 ICSE Questions and Answers PDF Download

The Trigonometry is considered to be a scoring chapter in ICSE Class 10 Maths syllabus as students can score good with proper practise. So for proper practice, students need to start solving Trigonometry Class 10 ICSE questions and answers; accordingly they can learn the formulas and derivations in a genuine manner. 

Trigonometry Class 10 ICSE Important Questions PDF

After completing the chapter of Trigonometry, students are advised to practise more and more questions. Students can access the Trigonometry Class 10 ICSE important questions PDF through the Selfstudys website and can solve it; after that they can also refer to solutions for self analysis. By referring to the solutions, students can eliminate the confusions regarding the chapter Trigonometry from their comfort zone. 

Where Can Students Find Trigonometry Class 10 ICSE Questions and Answers?

Students can find the Trigonometry Class 10 ICSE questions and answers from the Selfstudys website, steps to download are explained below: 

  • Visit the Selfstudys website.

Trigonometry Class 10 ICSE Questions, ICSE Trigonometry Class 10 Questions, Trigonometry Class 10 ICSE Questions and Answers, ICSE Trigonometry Class 10 Questions and Answers, ICSE Trigonometry Questions and Answers Class 10, Trigonometry Class 10 ICSE Important Questions PDF

  • Search for Free Study Materials and then search for CISCE from the given list.

Trigonometry Class 10 ICSE Questions, ICSE Trigonometry Class 10 Questions, Trigonometry Class 10 ICSE Questions and Answers, ICSE Trigonometry Class 10 Questions and Answers, ICSE Trigonometry Questions and Answers Class 10, Trigonometry Class 10 ICSE Important Questions PDF

  • Click Important Question from the list.

Trigonometry Class 10 ICSE Questions, ICSE Trigonometry Class 10 Questions, Trigonometry Class 10 ICSE Questions and Answers, ICSE Trigonometry Class 10 Questions and Answers, ICSE Trigonometry Questions and Answers Class 10, Trigonometry Class 10 ICSE Important Questions PDF

  • A new page will appear, Click on Class 10 and then select Maths from the list of subjects. 
  • Again a new page will appear where you can select the chapter Trigonometry from the list. 

Features of Trigonometry Class 10 ICSE Questions and Answers PDF

By regular solving Trigonometry Class 10 ICSE questions and answers PDF, students can identity the question pattern; below some of features are discussed:

  • Formulas are Discussed: In the Trigonometry Class 10 ICSE important questions PDF, formulas are discussed along with the derivations; accordingly students can understand formulas better. 
  • Various Types of Questions are Asked: Various types of important questions of Trigonometry are asked: data based questions, formula based questions, and many more. Through this students can understand the different approach to attempt different questions of Trigonometry. 
  • Hints and Solutions are Discussed: After solving the important questions of Trigonometry, it is obvious that students need to refer to answers so that they can analyse the mistakes. Hints and solutions of Trigonometry are discussed in the PDF provided in the Selfstudys website. 
  • Solved in a Stepwise Manner: The answers of Trigonometry questions are solved in a stepwise manner so that students can apply the same approach during the board exam and can score well. 
  • All Concepts are Covered: Through the questions of Trigonometry all concepts are covered; in that students can understand the concepts in a better way. 

How Can Trigonometry Class 10 ICSE Questions and Answers Help Students?

The Trigonometry Class 10 ICSE questions and answers can help students in many ways, some are discussed below: 

  • Can Improve Problem Solving Skills: Problem solving skills is the ability to implement best possible answers for the questions of Trigonometry. To improve the problem solving skills, students can solve more and more questions related to Trigonometry. 
  • Can Prepare for Exams: Students can utilise the Trigonometry Class 10 ICSE important questions to understand the concepts in a better way and accordingly can prepare well for exams. 
  • Can Identify the Areas of Weaknesses: By practising questions of Trigonometry, students can easily identify the topics where they feel confusion and accordingly can improve their understanding of the topic. 
  • Can Analyse the Answers: Solutions are provided for the questions of Trigonometry, accordingly students can analyse their own answers with the provided solutions.
  • Improves Higher Order Thinking Skills: Higher order thinking skill is the type of skill in which students can solve the problems of Trigonometry effectively with different kinds of ideas. 
  • Provides Conceptual Understanding: It is important for students to have a conceptual understanding of the topics included in the Trigonometry. But to have a conceptual understanding in Trigonometry, students can start practising important questions. 

When Is the Best Time to Solve Trigonometry Class 10 ICSE Questions and Answers?

The best time to start solving Trigonometry Class 10 ICSE questions and answers is generally depends on the student’s preference and learning style, students can follow the given guidelines below: 

  • After Completing the Concept: Students can start solving the questions of Trigonometry after completing each concept. Accordingly, that particular concept of Trigonometry can have a deeper understanding in a student's brain. 
  • To Build Confidence: It is advisable for students to gradually increase the level of questions related to Trigonometry then only they can build confidence. To increase the confidence level, students need to practise more and more questions related to Trigonometry. 
  • To Identify the Gaps: To identify the gaps while understanding the concepts of Trigonometry, students can start solving the questions and can try to eliminate those gaps. 
  • During the Class: While attending the class of Trigonometry, students need to be very focused so that they can understand the concepts better. For this purpose students can start solving questions of Trigonometry and can improve their focus. 
  • After Finishing the Chapter: Students can start solving questions of Trigonometry after finishing the chapters properly so that they can be more expert in understanding the concepts. 
  • To Complete Assessment Questions: Sometimes the questions of Trigonometry in internal assessments can be the same as the questions in the PDF. So by referring to the questions in the PDF, students can also complete assessment questions related to Trigonometry. 

How to Score Better in Trigonometry Class 10 ICSE Important Questions? 

It is very important for students to perform well in the Trigonometry Class 10 ICSE important questions so, in that case, they can follow the given tips: 

  • Understand the Concepts: First and foremost step to perform well in Trigonometry Class 10 ICSE important questions is that students need to understand the concepts in a proper and better way. 
  • Have a Regular Practice of Questions: To perform well, students need to practise the Trigonometry questions, then only they can learn the different approach and can improve day by day. 
  • Use Formulas: Whenever there is a need, students should use relevant formulas then only they can score well in Trigonometry important questions. 
  • Match the Answers: Students are advised to match their answers with the actual answers after attempting questions of Trigonometry. Then only they can analyse the mistakes and improve accordingly to score well in Trigonometry questions. 
  • Seek Help: If there is any difficulty in understanding the concepts of Trigonometry then it is a must to seek help from their concerned teachers then only students can improve their score. 
  • Identify the Weak Points: To perform well in questions of Trigonometry they need to first identify the weak points. After that they need to eliminate the weak point then only they can score well in Trigonometry questions. 

The Impact of Trigonometry Class 10 ICSE Questions and Answers in the Preparation

The Trigonometry Class 10 ICSE questions and answers can have a significant impact on the preparations, some of them are discussed below: 

  • Improves Preciseness: Preciseness means to maintain the accuracy and correctness of any question; students can maintain preciseness by solving questions of Trigonometry on a regular basis.  
  • Improves Learning Process: Every student has a different learning process: different learning style; to complete the chapter Trigonometry. So to improve the learning process, students can solve important questions of Trigonometry.  
  • Reduces Confusions: To reduce confusions related to Trigonometry, students need to practise important questions. Clearing of doubts and confusions can make the preparation of Trigonometry a two way process. 
  • Provides Instant Result: Practising the important questions from Trigonometry Important Questions and Answers PDF can help students to get instant results or answers. After the instant result, students can easily improve in the preparation of Trigonometry. 
  • Helps in Consistency: In a student's life one needs to be very consistent while preparing for Class 10 Trigonometry then can perform well in the board exam. The consistency can be easily improved by solving questions of Trigonometry on a regular basis. In addition to this one, the ICSE Class 10 Maths Notes   can help students maintain consistency.
  • Uncomplicated Language: The questions of the Trigonometry are very easy so that students can understand word to word without any difficulty. 

How to Practise Trigonometry Class 10 ICSE Questions Effectively?

To practise Trigonometry Class 10 ICSE questions effectively, students need to follow some steps, those steps are: 

  • Cover the Chapter: To practise questions of Trigonometry effectively, they need to cover the chapter from the textbook, it is advisable for students to complete each and every concept.  
  • Start With Easy Questions: Students are advised to start with easy questions of Trigonometry and then gradually move on to the difficult ones. Through this students can solve the Trigonometry Class 10 ICSE important questions effectively. 
  • Set a Timer: While solving questions of Trigonometry, students need to set a timer so that they can feel the exam decorum; this can also help students to get used to time pressure and accordingly can improve the accuracy. 
  • Try to be Specific: It is advisable for students not to beat around the bush while solving questions of Trigonometry then only they can practise effectively. 
  • Read the Questions Carefully: Students are advised to read the questions of Trigonometry carefully so that they don’t miss out any word and can perform effectively.
  • Frame the Answers: Students are advised to frame their own answers while attempting questions of Trigonometry then only they can perform effectively. 

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  • Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics

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Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

Concise Mathematics Class 10 ICSE Solutions for Chapter 21 can be of great help while preparing for exams. The solutions are compiled by the subject experts and are extremely helpful for the students to understand Class 10 Chapter 21 Trigonometric Identities efficiently. Students can completely rely on ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions for a thorough understanding of the chapter as the solutions are prepared as the latest ICSE Class 10 syllabus and guidelines.

In Mathematics, trigonometric identities are considered equalities, which includes trigonometric functions and are valid for each value of the occurring variables where both sides of the equality are defined. Geometrically, trigonometric identities include certain functions of one or more angles. 

Learning the trigonometric identities efficiently with the help of ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions offered by Vedantu will definitely prove helpful for students preparing for board exams. Read below to know more about Concise Mathematics Class 10 ICSE Solutions for Chapter 21 Trigonometric Identities.

When trigonometric functions are used in an expression or equation, trigonometric Identities come in handy. Every value of a variable occurring on both sides of an equation is true for trigonometric identities. These identities are geometrically related to specific trigonometric functions (such as sine, cosine, and tangent) of one or more angles.

The major trigonometry functions are sine, cosine, and tangent, while the other three functions are cotangent, secant, and cosecant. All six trig functions are used to create trigonometric identities.

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Download ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions Free PDF

Students who are looking for accurate and exclusive ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions can refer to this article and download the solutions for free in PDF format. Students must go through all these detailed solutions to understand Chapter 21 concepts clearly and manage their exam Class 10 board exam preparation efficiently.

Designed and developed by professionals at Vedantu, ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions Free PDF includes comprehensive solutions to all the questions covered in the chapter. All the solutions are explained with help of relevant diagrams and are reviewed by the subject experts to bring reliable and error-free content for the students.

Students can download ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions free PDF with just a single click on the PDF link provided and access it anytime and anywhere as per their convenience.

How ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions is Helpful for Students?

The free and comprehensive ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions in a PDF format provided by Vedantu are structured precisely to clear the concepts of students easily. These solutions will surely give a clear understanding of the chapter to students.

Our Class 10 Mathematics Chapter 22 Selina Concise solutions are explained with the help of diagrams in a stepwise method which will help students to resolve their doubts in a precise manner. The solutions provided in the PDF provided the required information in a concise manner.

Our free ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions increase the level of confidence among Class 10 students and help them to get good marks in the examination.

The solutions will not merely benefit students to prepare for school exams, but also prepare them to face other competitive exams taken after school.

ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions provided on this page can be downloaded in a PDF format for free of cost and can be accessed anytime and anywhere without any difficulties.

In addition to the above solutions, students are also suggested to refer to ICSE Class 10 sample papers, previous year question papers and chapter - wise important questions offered by Vedantu. All these study materials can be easily accessed from Vedantu's official website or Vedantu app.

FAQs on Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics

1. How will ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions PDF will Help me to get Good Grades in Exams?

By referring to ICSE Mathematics Class 10 Chapter 21 Selina Concise Solutions PDF, you can resolve all your chapter doubts and queries instantly. The PDF is prepared by the subject experience teacher and will give you a better idea of how to represent Maths Solution Class 10 ICSE board exams. Optimum use of the PDF along with the proper revision will enhance your self-confidence and ace your Mathematics board exam.

2. Is it Mandatory to Solve ICSE Class 10 Mathematics Selina Concise Questions of all the Chapters?

Solving these questions can yield great benefits. Ideally, try to attempt all the Class 10 Mathematics Selina Concise questions first by your own. If you can't, then refer to ICSE Class 10 Mathematics Selina Concise Chapter-wise solutions offered by Vedantu. Rather than mugging up the Mathematics questions, it is essential to understand the concept and enhance your problem- solving skill. The solutions provided are just for reference.

3. What are trigonometric identities?

Trigonometric Identities are equalities involving trigonometry functions that hold for all values of the variables in the equation.

There are several different trigonometric identities that involve the side length and angle of a triangle. Only the right-angle triangle is subject to the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are the mathematical terms for sine, cosine, tangent, cosecant, secant, and cotangent. The sides of the right triangle, such as the adjacent, opposing, and hypotenuse sides, are used to define all of these trigonometric ratios. You can learn more about trigonometric identities from Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics.

4. What are the basic guidelines to proving trigonometric identities?

Proving a trigonometric identity entails demonstrating that the identity holds regardless of the value of xx or theta employed.

We cannot just substitute in a few xx numbers to "prove" that they're equal because it has to hold true for all values of xx. It's possible that both sides are equal at numerous points (for example, when solving the equation), leading us to believe we have a true identity.

Instead, we must employ logical procedures to demonstrate that one side of the equation may be changed into the other. We'll sometimes work on each side separately until they meet in the middle.

5. What is the general approach to proving trigonometric identities? 

Different trigonometric identities, such as reciprocal trigonometric functions and Pythagorean identities, should be recognisable to you.

There are numerous methods for proving one's identification. If you get stuck, here are some pointers:

1) Focus on the more difficult side of the equation. Try to make it as simple as possible.

2) If possible, replace all trigonometric functions with sin theta and cos theta.

3) Recognize algebraic operations such as factoring, expanding, applying the distributive property, and multiplying and adding fractions. This allows us to further reduce the phrase.

4) Make use of the different trigonometric identities. Keep an eye out for the Pythagorean identity in particular.

5) Collaborate on all sides.

6) Keep an eye on the opposite side of the equation and work toward it.

7) Take into account the "trigonometric conjugate."

6. What are the complementary and supplementary trigonometric identities?

Complementary angles are a pair of two angles whose sum equals 90 degrees. (90 - ) is the complement of an angle. Complementary angle trigonometric ratios are as follows:

sin (90°- θ) = cos θ

cos (90°- θ) = sin θ

cosec (90°- θ) = sec θ

sec (90°- θ) = cosec θ

tan (90°- θ) = cot θ

cot (90°- θ) = tan θ

The supplementary angles are a pair of two angles whose sum equals 180 degrees. An angle's supplement is equal to (180 -). Supplementary angle trigonometric ratios are as follows:

sin (180°- θ) = sinθ

cos (180°- θ) = -cos θ

cosec (180°- θ) = cosec θ

sec (180°- θ)= -sec θ

tan (180°- θ) = -tan θ

cot (180°- θ) = -cot θ

7. How to prepare for trigonometric identities?

To prepare for trigonometric identities, it is imperative for students to learn the fundamentals of trigonometry completely. The foundation needs to be strong for building the knowledge further. Students must make sure that they remember the formulas. Without learning the formulas, students will not be able to solve problems related to trigonometric identities. To consolidate their knowledge further, students should solve sample papers and questions related to trigonometric identities. Students can find free study materials and sample papers on the Vedantu app and website.

  • ICSE Class 10
  • ICSE Class 10 Selina Solutions
  • ICSE Class 10 Maths Selina Solution
  • Chapter 21 Trigonometrical Identities

Selina Solutions Concise Maths Class 10 Chapter 21 Trigonometrical Identities

The science which deals with the measurements of triangles is called trigonometry. Trigonometrical ratios and its relations are used to prove trigonometric identities. Further, the trigonometrical ratios of complementary angles and the use of trigonometrical tables are the other topics covered in this chapter. As this chapter lays foundation to higher class Mathematics, students should acquire a strong grip over this chapter. For this purpose, BYJU’S has created the Selina Solutions for Class 10 Mathematics prepared by expert faculty having vast academic experience. This also improves the problem-solving skills of students, which are crucial from an examination point of view. The Selina Solutions for Class 10 Mathematics Chapter 21 Trigonometrical Identities PDF are available exercise-wise in the links given below.

Selina Solutions Concise Maths Class 10 Chapter 21 Trigonometrical Identities Download PDF

selina-sol-maths-class-10-ch-21-ex-a-1

Exercises of Concise Selina Solutions Class 10 Maths Chapter 21 Trigonometrical Identities

Exercise 21(A) Solutions

Exercise 21(B) Solutions

Exercise 21(C) Solutions

Exercise 21(D) Solutions

Exercise 21(E) Solutions

Access Selina Solutions Concise Maths Class 10 Chapter 21 Trigonometrical Identities

Exercise 21(A) Page No: 237

Prove the following identities:

1. sec A – 1/ sec A + 1 = 1 – cos A/ 1 + cos A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 1

– Hence Proved

2. 1 + sin A/ 1 – sin A = cosec A + 1/ cosec A – 1

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 2

3. 1/ tan A + cot A = cos A sin A

Taking L.H.S,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 3

4. tan A – cot A = 1 – 2 cos 2 A/ sin A cos A

Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 4

5. sin 4 A – cos 4 A = 2 sin 2 A – 1

sin 4 A – cos 4 A

= (sin 2 A) 2 – (cos 2 A) 2

= (sin 2 A + cos 2 A) (sin 2 A – cos 2 A)

= sin 2 A – cos 2 A

= 2sin 2 A – 1

6. (1 – tan A) 2 + (1 + tan A) 2 = 2 sec 2 A

(1 – tan A) 2 + (1 + tan A) 2

= (1 + tan 2 A + 2 tan A) + (1 + tan 2 A – 2 tan A)

= 2 (1 + tan 2 A)

7. cosec 4 A – cosec 2 A = cot 4 A + cot 2 A

cosec 4 A – cosec 2 A

= cosec 2 A(cosec 2 A – 1)

= (1 + cot 2 A) (1 + cot 2 A – 1)

= (1 + cot 2 A) cot 2 A

= cot 4 A + cot 2 A = R.H.S

8. sec A (1 – sin A) (sec A + tan A) = 1

sec A (1 – sin A) (sec A + tan A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 5

9. cosec A (1 + cos A) (cosec A – cot A) = 1

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 6

10. sec 2 A + cosec 2 A = sec 2 A . cosec 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 7

11. (1 + tan 2 A) cot A/ cosec 2 A = tan A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 8

12. tan 2 A – sin 2 A = tan 2 A. sin 2 A

tan 2 A – sin 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 9

13. cot 2 A – cos 2 A = cos 2 A. cot 2 A

cot 2 A – cos 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 10

14. (cosec A + sin A) (cosec A – sin A) = cot 2 A + cos 2 A

(cosec A + sin A) (cosec A – sin A)

= cosec 2 A – sin 2 A

= (1 + cot 2 A) – (1 – cos 2 A)

= cot 2 A + cos 2 A = R.H.S

15. (sec A – cos A)(sec A + cos A) = sin 2 A + tan 2 A

(sec A – cos A)(sec A + cos A)

= (sec 2 A – cos 2 A)

= (1 + tan 2 A) – (1 – sin 2 A)

= sin 2 A + tan 2 A = RHS

16. (cos A + sin A) 2 + (cosA – sin A) 2 = 2

(cos A + sin A) 2 + (cosA – sin A) 2

= cos2 A + sin2 A + 2cos A sin A + cos2 A – 2cosA.sinA

= 2 (cos 2 A + sin 2 A) = 2 = R.H.S

17. (cosec A – sin A)(sec A – cos A)(tan A + cot A) = 1

(cosec A – sin A)(sec A – cos A)(tan A + cot A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 11

18. 1/ sec A + tan A = sec A – tan A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 12

19. cosec A + cot A = 1/ cosec A – cot A

cosec A + cot A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 13

20. sec A – tan A/ sec A + tan A = 1 – 2 secA tanA + 2 tan 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 14

= 1 + tan 2 A + tan 2 A – 2 sec A tan A

= 1 – 2 sec A tan A + 2 tan 2 A = RHS

21. (sin A + cosec A) 2 + (cos A + sec A) 2 = 7 + tan 2 A + cot 2 A

(sin A + cosec A) 2 + (cos A + sec A) 2

= sin 2 A + cosec 2 A + 2 sin A cosec A + cos 2 A + sec 2 A + 2cos A sec A

= (sin 2 A + cos 2 A ) + cosec 2 A + sec 2 A + 2 + 2

= 1 + cosec 2 A + sec 2 A + 4

= 5 + (1 + cot 2 A) + (1 + tan 2 A)

= 7 + tan 2 A + cot 2 A = RHS

22. sec 2 A. cosec 2 A = tan 2 A + cot 2 A + 2

RHS = tan 2 A + cot 2 A + 2 = tan 2 A + cot 2 A + 2 tan A. cot A

= (tan A + cot A) 2 = (sin A/cos A + cos A/ sin A) 2

= (sin2 A + cos2 A/ sin A.cos A) 2 = 1/ cos 2 A. sin 2 A

= sec 2 A. cosec 2 A = LHS

23. 1/ 1 + cos A + 1/ 1 – cos A = 2 cosec 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 15

24. 1/ 1 – sin A + 1/ 1 + sin A = 2 sec 2 A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(A) - 16

Exercise 21(B) Page No: 237

1. Prove that:

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(B) - 1

(ii) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(B) - 3

(v) Taking LHS,

2 sin 2 A + cos 2 A

= 2 sin 2 A + (1 – sin 2 A) 2

= 2 sin 2 A+ 1 + sin 4 A – 2 sin 2 A

= 1 + sin 4 A = RHS

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(B) - 6

2. If x cos A + y sin A = m and x sin A – y cos A = n, then prove that:

x 2 + y 2 = m 2 + n 2  

Taking RHS,

= (x cos A + y sin A) 2 + (x sin A – y cos A) 2

= x 2 cos 2 A + y 2 sin 2 A + 2xy cos A sin A + x 2 sin 2 A + y 2 cos 2 A – 2xy sin A cos A

= x 2 (cos 2 A + sin 2 A) + y 2 (sin 2 A + cos 2 A)

3. If m = a sec A + b tan A and n = a tan A + b sec A, prove that m 2 – n 2 = a 2 – b 2

= (a sec A + b tan A) 2 – (a tan A + b sec A) 2

= a 2 sec 2 A + b 2 tan 2 A + 2 ab sec A tan A – a 2 tan 2 A – b 2 sec 2 A – 2ab tan A sec A

= a 2 (sec 2 A – tan 2 A) + b 2 (tan 2 A – sec 2 A)

= a 2 – b 2

Exercise 21(C) Page No: 328

1. Show that:

(i) tan 10 o tan 15 o tan 75 o tan 80 o = 1

Taking, tan 10 o tan 15 o tan 75 o tan 80 o

= tan (90 o – 80 o ) tan (90 o – 75 o ) tan 75 o tan 80 o

= cot 80 o cot 75 o tan 75 o tan 80 o

(ii) sin 42 o sec 48 o + cos 42 o cosec 48 o = 2

Taking, sin 42 o sec 48 o + cos 42 o cosec 48 o

= sin 42 o sec (90 o – 42 o ) + cos 42 o cosec (90 o – 42 o )

= sin 42 o cosec 42 o + cos 42 o sec 42 o

(iii) sin 26 o / sec 64 o + cos 26 o / cosec 64 o = 1

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(C) - 1

2. Express each of the following in terms of angles between 0°and 45°:

(i) sin 59°+ tan 63°

(ii) cosec 68°+ cot 72°

(iii) cos 74°+ sec 67°

= sin (90 – 31)°+ tan (90 – 27)°

= cos 31°+ cot 27°

= cosec (90 – 22)°+ cot (90 – 18)°

= sec 22°+ tan 18°

(iii) cos 74°+ sec 67°

= cos (90 – 16)°+ sec (90 – 23)°

= sin 16°+ cosec 23°

3. Show that:

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(C) - 2

= sin A cos A – sin 3 A cos A – cos 3 A sin A

= sin A cos A – sin A cos A (sin 2 A + cos 2 A)

4. For triangle ABC, show that:

(i) sin (A + B)/ 2 = cos C/2

(ii) tan (B + C)/ 2 = cot A/2

We know that, in triangle ABC

(∠A + ∠B)/ 2 = 90 o – ∠C/ 2

sin ((A + B)/ 2) = sin (90 o – C/ 2)

(∠C + ∠B)/ 2 = 90 o – ∠A/ 2

tan ((B + C)/ 2) = tan (90 o – A/ 2)

5. Evaluate:

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(C) - 4

(ii) 3 cos 80 o cosec 10 o + 2 cos 59 o cosec 31 o

= 3 cos (90 – 10) o cosec 10 o + 2 cos (90 – 31) o cosec 31 o

= 3 sin 10 o cosec 10 o + 2 sin 31 o cosec 31 o

= 3 + 2 = 5

(iii) sin 80 o / cos 10 o + sin 59 o sec 31 o

= sin (90 – 10) o / cos 10 o + sin (90 – 31) o sec 31 o

= cos 10 o / cos 10 o + cos 31 o sec 31 o

= 1 + 1 = 2

(iv) tan (55 o – A) – cot (35 o + A)

= tan [90 o – (35 o + A)] – cot (35 o + A)

= cot (35 o + A)] – cot (35 o + A)

(v) cosec (65 o + A) – sec (25 o – A)

= cosec [90 o – (25 o – A)] – sec (25 o – A)

= sec (25 o – A) – sec (25 o – A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(C) - 6

= 1 – 2 = -1

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(C) - 8

(ix) 14 sin 30 o + 6 cos 60 o – 5 tan 45 o

= 14 (1/2) + 6 (1/2) – 5(1)

= 7 + 3 – 5

6. A triangle ABC is right angled at B; find the value of (sec A. cosec C – tan A. cot C)/ sin B

As, ABC is a right angled triangle right angled at B

So, A + C = 90 o

(sec A. cosec C – tan A. cot C)/ sin B

= (sec (90 o – C). cosec C – tan (90 o – C). cot C)/ sin 90 o

= (cosec C. cosec C – cot C. cot C)/ 1 = cosec 2 C – cot 2 C

Exercise 21(D) Page No: 331

1. Use tables to find sine of:

(ii) 34° 42′

(iii) 47° 32′

(iv) 62° 57′

(v) 10° 20′ + 20° 45′

(i) sin 21 o  = 0.3584

(ii) sin 34 o  42’= 0.5693

(iii) sin 47 o  32’= sin (47 o  30′ + 2′) =0.7373 + 0.0004 = 0.7377

(iv) sin 62 o  57′ = sin (62 o  54′ + 3′) = 0.8902 + 0.0004 = 0.8906

(v) sin (10 o  20′ + 20 o  45′) = sin 30 o 65′ = sin 31 o 5′ = 0.5150 + 0.0012 = 0.5162

2. Use tables to find cosine of:

(ii) 8° 12’

(iii) 26° 32’

(iv) 65° 41’

(v) 9° 23’ + 15° 54’

(i) cos 2° 4’ = 0.9994 – 0.0001 = 0.9993

(ii) cos 8° 12’ = cos 0.9898

(iii) cos 26° 32’ = cos (26° 30’ + 2’) = 0.8949 – 0.0003 = 0.8946

(iv) cos 65° 41’ = cos (65° 36’ + 5’) = 0.4131 -0.0013 = 0.4118

(v) cos (9° 23’ + 15° 54’) = cos 24° 77’ = cos 25° 17’ = cos (25° 12’ + 5’) = 0.9048 – 0.0006 = 0.9042

3. Use trigonometrical tables to find tangent of:

(ii) 42° 18′

(iii) 17° 27′

(i) tan 37 o  = 0.7536

(ii) tan 42 o  18′ = 0.9099

(iii) tan 17 o   27′ = tan (17 o  24′ + 3′) = 0.3134 + 0.0010 = 0.3144

Exercise 21(E) Page No: 332

1. Prove the following identities:

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 1

(i) Taking LHS,

1/ (cos A + sin A) + 1/ (cos A – sin A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 2

(ii) Taking LHS, cosec A – cot A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 3

(iii) Taking LHS, 1 – sin 2 A/ (1 + cos A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 4

(iv) Taking LHS,

(1 – cos A)/ sin A + sin A/ (1 – cos A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 5

(v) Taking LHS, cot A/ (1 – tan A) + tan A/ (1 – cot A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 6

(vi) Taking LHS, cos A/ (1 + sin A) + tan A

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 7

(vii) Consider LHS,

= (sin A/(1 – cos A)) – cot A

We know that, cot A = cos A/sin A

So, = (sin 2 A – cos A + cos 2 A)/(1 – cos A) sin A

= (1 – cos A)/(1 – cos A) sin A

(viii) Taking LHS, (sin A – cos A + 1)/ (sin A + cos A – 1)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 8

(ix) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 9

(x) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 10

(xi) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 11

(xii) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 12

(xiii) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 13

(xiv) Taking LHS,

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 14

(xv) Taking LHS,

sec 4 A (1 – sin 4 A) – 2 tan 2 A

= sec 4 A(1 – sin 2 A) (1 + sin 2 A) – 2 tan 2 A

= sec 4 A(cos 2 A) (1 + sin 2 A) – 2 tan 2 A

= sec 2 A + sin 2 A/ cos 2 A – 2 tan 2 A

= sec 2 A – tan 2 A

(xvi) cosec 4 A(1 – cos 4 A) – 2 cot 2 A

= cosec 4 A (1 – cos 2 A) (1 + cos 2 A) – 2 cot 2 A

= cosec 4 A (sin 2 A) (1 + cos 2 A) – 2 cot 2 A

= cosec 2 A (1 + cos 2 A) – 2 cot 2 A

= cosec 2 A + cos 2 A/sin 2 A – 2 cot 2 A

= cosec 2 A + cot 2 A – 2 cot 2 A

= cosec 2 A – cot 2 A

(xvii) (1 + tan A + sec A) (1 + cot A – cosec A)

= 1 + cot A – cosec A + tan A + 1 – sec A + sec A + cosec A – cosec A sec A

= 2 + cos A/sin A+ sin A/cos A – 1/(sin A cos A)

= 2 + (cos 2 A + sin 2 A)/ sin A cos A – 1/(sin A cos A)

= 2 + 1/(sin A cos A) – 1/(sin A cos A)

2. If sin A + cos A = p

and sec A + cosec A = q, then prove that: q(p 2 – 1) = 2p

Taking the LHS, we have

= 2sin A + 2 cos A

3. If x = a cos θ and y = b cot θ, show that:

a 2 / x 2 – b 2 / y 2 = 1

a 2 / x 2 – b 2 / y 2

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 15

4. If sec A + tan A = p, show that:

sin A = (p 2 – 1)/ (p 2 + 1)

Taking RHS, (p 2 – 1)/ (p 2 + 1)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 25

5. If tan A = n tan B and sin A = m sin B, prove that:

cos 2 A = m 2 – 1/ n 2 – 1

tan A = n tan B

n = tan A/ tan B

And, sin A = m sin B

m = sin A/ sin B

Now, taking RHS and substitute for m and n

m 2 – 1/ n 2 – 1

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 16

6. (i) If 2 sin A – 1 = 0, show that:

sin 3A = 3 sin A – 4 sin 3 A

(ii) If 4 cos 2 A – 3 = 0, show that:

cos 3A = 4 cos 2 A – 3 cos A

(i) Given, 2 sin A – 1 = 0

So, sin A = ½

We know, sin 30 o = 1/2

Hence, A = 30 o

Now, taking LHS

sin 3A = sin 3(30 o ) = sin 30 o = 1

RHS = 3 sin 30 o – 4 sin 3 30 o = 3 (1/2) – 4 (1/2) 3 = 3 – 4(1/8) = 3/2 – ½ = 1

Therefore, LHS = RHS

(ii) Given, 4 cos 2 A – 3 = 0

4 cos 2 A = 3

cos 2 A = 3/4

cos A = √3/2

We know, cos 30 o = √3/2

Now, taking

LHS = cos 3A = cos 3(30 o ) = cos 90 o = 0

RHS = 4 cos 3 A – 3 cos A = 4 cos 3 30 o – 3 cos 30 o = 4 (√3/2) 3 – 3 (√3/2)

= 4 (3√3/8) – 3√3/2

= 3√3/2 – 3√3/2

7. Evaluate:

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 17

= 2 (1) 2 + 1 2 – 3

= 2 + 1 – 3 = 0

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 19

(iv) cos 40 o cosec 50 o + sin 50 o sec 40 o

= cos (90 – 50) o cosec 50 o + sin (90 – 50) o sec 40 o

= sin 50 o cosec 50 o + cos 40 o sec 40 o

(v) sin 27 o sin 63 o – cos 63 o cos 27 o

= sin (90 – 63) o sin 63 o – cos 63 o cos (90 – 63) o

= cos 63 o sin 63 o – cos 63 o sin 63 o

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 21

(vii) 3 cos 80 o cosec 10 o + 2 cos 59 o cosec 31 o

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 22

8. Prove that:

(i) tan (55 o + x) = cot (35 o – x)

(ii) sec (70 o – θ) = cosec (20 o + θ)

(iii) sin (28 o + A) = cos (62 o – A)

(iv) 1/ (1 + cos (90 o – A)) + 1/(1 – cos (90 o – A)) = 2 cosec 2 (90 o – A)

(v) 1/ (1 + sin (90 o – A)) + 1/(1 – sin (90 o – A)) = 2 sec 2 (90 o – A)

(i) tan (55 o + x) = tan [90 o – (35 o – x)] = cot (35 o – x)

(ii) sec (70 o – θ ) = sec [90 o – (20 o + θ )] = cosec (20 o + θ )

(iii) sin (28 o + A) = sin [90 o – (62 o – A)] = cos (62 o – A)

Selina Solutions Concise Class 10 Maths Chapter 21 ex. 21(E) - 23

The given solutions are as per the 2019-20 Concise Selina textbook. The Selina Solutions for the academic year 2023-24 will be updated soon.

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ICSE 10th Maths Important Questions

Icse important questions for class 10 maths- chapter wise questions.

Important Questions for Class 10 Maths are provided (Chapter wise) for your ICSE 10th board examination, to help you be a master in the subject. If you are going to sit for any competitive exams or your boards, then these Chapter wise questions set can help you achieve good marks for sure. The books are made interactive and interesting for class 10th Maths students to amplify their conceptual knowledge and prepare them for all sorts of questions in the ICSE 10th board examination.

A lot of fun activities are included in between the chapters to help the students learn in a playful manner and gain knowledge more efficiently.

The important questions for Maths class 10th by SpeedLabs are designed exclusively for the students to get an idea of the question pattern and overview of the syllabus given in the ICSE Class 10 Maths exercises.

You can also download Solved Examples for Class 10 Maths to be an expert and score well in your ICSE 10th board examination.

  • Chapter 1- Goods and Service Tax (GST)
  • Chapter 2 – Banking 
  • Chapter 3 – Linear Equations
  • Chapter 4 – Quadratic Equations in One Variable 
  • Chapter 5 – Ratio and Proportion
  • Chapter 6 – Factorization
  • Chapter 7 -Matrices
  • Chapter 8 – Arithmetic Progression 
  • Chapter 9 – Co-ordinate Geometry
  • Chapter 10 – Similarity
  • Chapter 11 – Circles
  • Chapter 12 – Angle Properties
  • Chapter 13 – Cyclic Properties
  • Chapter 14 – Tangent and Secant Properties 
  • Chapter 15 – Constructions
  • Chapter 16 -Area and volume of solids – Cylinder, Cone and Sphere.
  • Chapter 17 –  Trigonometry
  • Chapter 18 -Statistics
  • Chapter 19 – Probability

Chapter-wise Important Questions for ICSE Class 10 Maths:

Chapter 1: Goods and Service Tax (GST) – GST or Goods and Services Tax, is one of the most important chapters for ICSE Class 10th Maths. It is an indirect tax imposed on the supply of goods and services. There are three types of GST:

Check out this link for important questions from GST for ICSE Class 10 Maths.

Chapter 2: Banking-

The business of receiving money from depositors (or account holders), safeguarding, and lending money to businesses or individuals is called banking. There Banks are institutions that carry out the business of taking deposits and lending money. Check out this link for important questions from Banking for ICSE Class 10 Maths.

Chapter 3: Linear Equations-

In Class 10 Chapter 3, an equation of the form Ax+ By +C= 0 is called a linear equation in two variables x and y where A, B, and C are real numbers. When two linear equations are in the same two variables, they are called a pair of linear equations in two variables. Check out this link for important questions from Linear Equations for ICSE Class 10 Maths.

Chapter 4: Quadratic Equations in One Variable-

The standard form of a quadratic equation is ax2+bx+c=0, where a, b and c are real numbers and “a” is not equal to 0. In this form, it is easy to see that “a” is the coefficient of x2 and is known as the quadratic coefficient. Whereas “b” is the coefficient of x and it is known as the linear coefficient. “C” is constant. Check out this link for important questions from Quadratic Equations in One Variable for ICSE Class 10 Maths.

Chapter 5: Ratio and Proportion-

ICSE 10th Maths is impossible without having proper knowledge about this chapter. A ratio is an ordered pair of numbers x and y, written x / y where y is not equal to 0. A proportion is an equation that has two ratios set equal to each other. Check out this link for important questions from Ratio and Proportion for ICSE Class 10 Maths.

Chapter 6: Factorization-

If you are planning to sit for JEE in the future, then you should master yourself in Factorisation. While doing factorization, we reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors. The factors of any particular equation can be an integer, a single variable, or an algebraic expression itself. Check out this link for important questions from Factorisation for ICSE Class 10 Maths.

Chapter 7: Matrices-

In Matrix, a set of numbers arranged in rows and columns so as to form a rectangular assembling. The numbers are called the elements of the matrix. Matrices have wide application in engineering, economics, physics, and statistics as well as in other branches of maths. Check out this link for important questions from Matrices for ICSE Class 10 Maths.

Chapter 8: Arithmetic Progression-

Arithmetic Progression (AP) is a chronological sequence of numbers in which the difference between any two numbers is constant. Check out this link for important questions from Arithmetic Progression for ICSE Class 10 Maths.

Chapter 9: Coordinate Geometry-

Class 10th, Coordinate Geometry is one of the most important chapters not only for your boards but also keeping in mind the JEE syllabus. Coordinate Geometry is also called Cartesian Geometry. It helps you to find the distance between two points whose coordinates are being provided. Check out this link for important questions from Co-ordinate Geometry for ICSE Class 10 Maths.

Chapter 10: Similarity-

In class 10th Maths, Chapter 10 “Similarity” is defined by two triangles that are being given; they are said to be similar when their corresponding angles are equal and their corresponding sides are parallel. Check out this link for important questions from Co-ordinate Geometry for ICSE Class 10 Maths.

Chapter 11: Circles-

Circles are one of the most important chapters not only for boards but also for the jee syllabus that we will be studied in 11th and 12th grade as in this chapter we will come across properties related angles subtended by chords, segments, etc. Along with that, we will also grasp knowledge about the important concept of cyclic quadrilaterals, their properties, etc. Check out this link for important questions from Circles for ICSE Class 10 Maths.

Chapter 12: Angle Properties-

To crack any competitive exams in your future or your class 10th Maths exam, you need to be clear with your basic knowledge in Maths. Angle Properties is defined as the sum of all the angles on one side of a straight line always equals 180 degrees. Check out this link for important questions from Angle Properties for ICSE Class 10 Maths.

Chapter 13: Cyclic Properties-

In a Cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees. These are totally opposite to that of Angle Properties. In this chapter, we shall learn about the different Cyclic Properties in detail. Check out this link for important questions from Cyclic Properties for ICSE Class 10 Maths.

Chapter 14: Tangent and Secant Properties-

A tangent to a circle is a line that intersects the circle only at one point whereas a straight line that intersects a circle in two points is called a Secant. In this chapter, we can study the various properties of a Tangent and a Secant. Check out this link for important questions from Tangent and Secant Properties for ICSE Class 10 Maths.

Chapter 15: Constructions-

Class 10th chapter 14 “Constructions”, is one of the most important chapters not only for boards but also keeping in mind the JEE syllabus that we will be studying in 11th and 12th grade as well. In this chapter, we will learn how to construct triangles with different criteria, construction of angle bisectors, etc. Check out this link for important questions from Constructions for ICSE Class 10 Maths.

Chapter 16: Area and Volume of Solids- Cylinder, Cone and Sphere-

By surface area we mean the sum of the areas of all the closed surfaces of a solid. By Volume, we understand the capacity of a solid object. In this chapter we will learn about the Area and Volume of three different solids; Cylinder, Cone, and Sphere. Check out this link for important questions from Area and Volume of Solids for ICSE Class 10 Maths.

Chapter 17: Trigonometry-

Trigonometry is a branch of mathematics dealing with the lengths and angles of triangles. In simple words, it is the study of triangles. Check out this link for important questions from Trigonometry for ICSE Class 10 Maths.

Chapter 18: Statistics-

Class 10th chapter 2 “Polynomials” is one of the most important chapters not only for boards but also for keeping in mind the data analysis and managing it at various levels. In this chapter, we will also study important topics like mean, median, mode, variance, standard deviation, etc. Check out this link for important questions from Statistics for ICSE Class 10 Maths

Chapter 19: Probability-

Class 10th chapter 19 “Probability” is one of the most important chapters not only for ICSE boards but also we have to keep in mind about the JEE syllabus that we will be studying in 11th and 12th grade as in this chapter we will come across outcomes of various types of experiments, its occurrence, probability, etc. Check out this link for important questions from Probability for ICSE Class 10 Maths. [A small tip]:- Those who are preparing for Class 10 Maths exams, should practice solving more questions every day and clear every doubt prior to the examination. You can check the Online Video Solutions for Class 10 ICSE for Maths as well as other Science subjects provided by SpeedLabs. These detailed video lectures will ensure your quality performance in your ICSE 10th board exam and help you excel in your academics without much pressure and nervousness.

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  • Worksheet For class 10

ICSE worksheet for class 10 Maths

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Physics Wallah academic team prepared chapter wise ICSE Worksheet for Class 10 Maths with detail solutions. These ICSE Class 10 Maths Worksheet consist of all type of questions required to understand the concepts of class 10 Maths.

They get a clear idea of ​​the different concepts and how the questions are asked in the test. In addition, these ICSE Board Class 10 maths also help students review topics and improve their confidence level and the ability to write step-wise skills before exams.. All Worksheet for Class 10 science are with detail solutions for reference. For ICSE Class 10 Maths Solutions check out the page.

Find below Chapter Wise ICSE Worksheet for Class 10 Maths PDF

  • Practice Questions For ICSE Maths Chapter-Banking
  • Practice Questions For ICSE Maths Chapter-Compound interest
  • Practice Questions For ICSE Maths Chapter-Distance and section formula
  • Practice Questions For ICSE Maths Chapter-Equation of a straight line
  • Practice Questions For ICSE Maths Chapter-Graphical representation
  • Practice Questions For ICSE Maths Chapter-linear in equations in one variable
  • Practice Questions For ICSE Maths Chapter-Matrices
  • Practice Questions For ICSE Maths Chapter-Measures of central tendency
  • Practice Questions For ICSE Maths Chapter-Mensuration
  • Practice Questions For ICSE Maths Chapter-Probability
  • Practice Questions For ICSE Maths Chapter-Quadratic equations
  • Practice Questions For ICSE Maths Chapter-Ratio and proportion
  • Practice Questions For ICSE Maths Chapter-Reflection
  • Practice Questions For ICSE Maths Chapter-Sales tax and value added tax
  • Practice Questions For ICSE Maths Chapter-shares and dividends
  • Practice Questions For ICSE Maths Chapter-similarity
  • Practice Questions For ICSE Maths Chapter-symmetry
  • Practice Questions For ICSE Maths Chapter-Trigonometry
  • Practice Questions For ICSE Maths Chapter-use of factor theorem

Benefits of practising ICSE Worksheet Class 10 Maths

  • Provides an idea of ​​the marking weightage of each section, the key questions, and the number of questions on each topic.
  • A worksheet will help students familiarize themselves with the different types of questions in each chapter to make their ideas clear.
  • Students can analyze their performance and work on their weak points.
  • It gives them confidence as they try out the final question paper.

ICSE Worksheet class 10

Chapter Wise Worksheet for ICSE Class 10 Maths

  • Compound Interest
  • Distance and Section formula
  • Equation of a Straight Line
  • Graphical Representation
  • Linear Eqautions in one
  • Measues of Central Tendency
  • Mensuration
  • Probability
  • Quadratic Equations
  • Ration and Proportions
  • Sales Tax and Value added Tax
  • Shares and Dividends
  • Trigonometry
  • Use of Factor Theorem

ICSE is a very tough board. The ICSE curriculum is based on the current state of education, and the board updates its syllabus from time to time. ICSE syllabus is well-balanced and helpful for students. It involves appropriate curriculum assessment so that students can learn each subject in both ways - theory and practically. The ICSE worksheet for Class 10 provides students with a good learning experience in all its categories. Students can download the ICSE Worksheet for Class 10 Maths and use it to prepare for their exams.

Related Link

  • Class 10 Physics Notes
  • Class 10 Chemistry Notes
  • Class 10 Biology Notes
  • Class 10 Maths Notes
  • Chapter Wise Quiz Class 10 Physics
  • Chapter Wise Quiz Class 10 Chemistry
  • Chapter Wise Quiz Class 10 Biology
  • Chapter Wise Quiz Class 10 Maths
  • Previous year Board Papers
  • Sample Papers Maths Class 10
  • Sample Papers Science Class 10
  • NCERT Maths Solutions Class-10

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Trigonometry – ICSE Solutions for Class 10 Mathematics

ICSE Solutions Selina ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 18 Trigonometry for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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ICSE /Class 10

Maths mcq based on   trigonometry.

Our free online Maths test quiz for Class 10, ICSE will assist you to improve your Maths skills on every concept in a fun interactive way.

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Solving MCQ Questions for ICSE Class 10 Maths With Answers on Just Tutors is the best way to revise and prepare for ICSE Class 10 Maths Examination.

MCQ Questions for ICSE Class 10 Maths With Answers

Just Tutors brings you topic wise MCQ Questions for ICSE Class 10 with all the subtopics from Trigonometry. Multiple Choice Questions for ICSE Class 10 Maths are available for free, you can test your knowledge anytime and share the links with your friends to help them check their knowledge.

Questions 10

Class 10-trigonometry : choose your sub topic, 1-using identities, 2-heights and distances.

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  6. Previous Years Questions (PYQs) || Trigonometry || Class 10 ICSE #boardexam #icseboard

COMMENTS

  1. Practice Questions ICSE Maths Chapter -Trigonometry

    This page consists of a worksheet for class 10 Maths of chapter-Trigonometry with an answer key. Chapter-Trigonometry needs additional practice to give aspirants quality questions and numerical of chapter-Trigonometry Academic team of Physics Wallah uploaded this worksheet.

  2. Class 10: Trigonometry

    Class 10: Trigonometry - Board Problems. Date: January 15, 2018 Author: ICSE CBSE ISC Board Mathematics Portal for Students 13 Comments. Answer: Answer: OR. Answer: Answer: Answer: ... Previous Previous post: 2011 ICSE (Class 10) Board Paper Solution: Mathematics. Next Next post: Class 10: ...

  3. Trigonometry

    Trigonometry - ICSE Solutions for Class 10 Mathematics ICSE Solutions Selina ICSE Solutions Get ICSE Solutions for Class 10 Mathematics Chapter 18 Trigonometry for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf.

  4. Class 10 Maths Chapter 18 Trigonometry Important Questions

    Here's an introduction to trigonometry in Class 10 ICSE mathematics: Importance of Trigonometry: Trigonometry is a critical branch of mathematics because it helps us solve real-world problems involving angles and distances. It's especially valuable in fields that require precise measurements and calculations. Common Trigonometric Formulas:

  5. Trigonometry Class 10 ICSE Questions and Answers PDF Download

    The Trigonometry is considered to be a scoring chapter in ICSE Class 10 Maths syllabus as students can score good with proper practise. So for proper practice, students need to start solving Trigonometry Class 10 ICSE questions and answers; accordingly they can learn the formulas and derivations in a genuine manner.

  6. Selina solutions for Concise Maths Class 10 ICSE chapter 21

    Selina solutions for Concise Maths Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise 21 (A) [Pages 324 - 325] Exercise 21 (A) | Q 1 | Page 324 Prove. sec A - 1 sec A + 1 = 1 - cos A 1 + cos A VIEW SOLUTION Exercise 21 (A) | Q 2 | Page 324 Prove. 1 + sin A 1 - sin A = c o sec A + 1 c o sin A - 1 VIEW SOLUTION

  7. ICSE solutions for Class 10 Mathematics chapter 18

    ICSE solutions for Mathematics Class 10 Mathematics CISCE 18 (Trigonometry) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams. Further, we at Shaalaa.com provide such solutions so students can prepare for written exams.

  8. Trigonometrical Identities Solutions for ICSE Board Class 10 ...

    Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics Last updated date: 04th Feb 2024 • Total views: 737.1k • Views today: 14.37k Download PDF NCERT Solutions CBSE CBSE Study Material Textbook Solutions Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

  9. Selina Concise Mathematics

    Selina Concise Mathematics - Part II Solutions for Class 10 Maths ICSE Chapter 21: Get free access to Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Class 10 Solutions which includes all the exercises with solved solutions. Visit TopperLearning now!

  10. ML Aggarwal Solutions for Class 10 Maths Chapter 18 Trigonometric

    1. If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigonometric identities). Solution: Given, sin A = 3/5 and A is an acute angle So, in ∆ABC we have ∠B = 90 o And, AC = 5 and BC = 3 By Pythagoras theorem, AB = √ (AC 2 - BC 2) = √ (5 2 - 3 2) = √ (25 - 9) = √ 16 = 4 Now, cos A = AB/AC = 4/5

  11. Free Maths Worksheets for ICSE Class 10

    Free Maths worksheets for the students of ICSE for Class 10 can practice and get these chapter wise Worksheet with solutions and download for free ... Worksheet ICSE Class 10 Maths Get Unlimited Practice for Maths on every topic ... Mensuration. 1 Topics | 4 Sub-Topics. Trigonometry. 2 Topics | 3 Sub-Topics. Statistics. 2 Topics | 6 Sub-Topics ...

  12. Selina Solutions Concise Mathematics Class 10 Chapter 21

    Solution: Taking L.H.S, - Hence Proved 4. tan A - cot A = 1 - 2 cos2 A/ sin A cos A Solution: Taking LHS, - Hence Proved 5. sin4 A - cos4 A = 2 sin2 A - 1

  13. ICSE 10th Maths Important Questions

    Chapter 15 - Constructions Chapter 16 -Area and volume of solids - Cylinder, Cone and Sphere. Chapter 17 - Trigonometry Chapter 18 -Statistics Chapter 19 - Probability Chapter-wise Important Questions for ICSE Class 10 Maths:

  14. Trigonometric Identities Multiple Choice Questions (MCQ's)

    Trigonometric Identities Multiple Choice Questions (MCQ's) Practice Tests. Timed Tests. Select the number of questions for the test: Multiple Choice Questions (MCQ) for Trigonometric Identities - ICSE Class 10 Maths on Topperlearning. These MCQ's are extremely critical for all ICSE students to score better marks.

  15. Selina Concise Mathematics Class 10 ICSE Solutions Trigonometrical

    Solution: Question 10. cot A−1 2−sec2 A = cot A 1+tan A. Solution: To prove that : cot A−1 2−sec2 A = cot A 1+tan A. Hence proved. Question 11. Solution: Question 12.

  16. ICSE worksheet for class 10 Maths

    These ICSE Class 10 Maths Worksheet consist of all type of questions required to understand the concepts of class 10 Maths. They get a clear idea of the different concepts and how the questions are asked in the test.

  17. Worksheets

    class 10 ICSE Math . Trigonometry Worksheet 1; Trigonometry Worksheet 1 solutions; Trigonometry Worksheet 2; Trigonometry Worksheet 2 solutions; GST Worksheet 1; GST Worksheet 2; GST Worksheet 2 Solutions; Physics. class 10 CBSE

  18. Trigonometry

    Without using trigonometric tables, evaluate. Question 9. From trigonometric tables, write the values of: Question 10. The string of a kite is 150 m long and it makes an angle of 60° with the horizontal. Find the height of the kite from the ground. Question 11. Solve the following equations: Question 12.

  19. MCQ Questions for ICSE Class 10 Math Chapter 5 Trigonometry

    Learn and practice concept wise tests from all subtopics of Trigonometry from ICSE Class 10 Maths . Solving MCQ Questions for ICSE Class 10 Maths With Answers on Just Tutors is the best way to revise and prepare for ICSE Class 10 Maths Examination. MCQ Questions for ICSE Class 10 Maths With Answers

  20. ML Aggarwal Trigonometric Identities Exe-18 Solutions ICSE Class-10

    ML Aggarwal Trigonometric Identities Exe-18 Solutions. ICSE Class-10 Maths Ch-18. Page-456. Question 1. If A is an acute angle and sin A = 3/5 find all other trigonometric ratios of angle A (using trigonometric identities).

  21. ICSE Curriculum for Class 10

    The ICSE Math class 10 math practice worksheets follow a stepwise learning process that helps students understand concepts better, recognize their mistakes, and eventually develop a strategy to tackle future problems. These interactive math questions for ICSE Math class 10 math also helps teachers and parents track the child's learning progress.

  22. ML Aggarwal Trigonometric Identities Chapter Test Solutions ICSE Class

    September 15, 2021 by PANDEY TUTORIAL. ML Aggarwal Trigonometric Identities Chapter Test Solutions ICSE Class-10 Maths Ch-18. We Provide Step by Step Answer of Chapter Test Trigonometric Identities Questions for ICSE Class-10 APC Understanding Mathematics. Visit official Website CISCE for detail information about ICSE Board Class-10.

  23. Trigonometrical Identities RS Aggarwal Goyal Brothers

    Step by Step Solutions of Chapter-22 Trigonometrical Identities RS Aggarwal Goyal Brothers is given to understand the topic clearly . Chapter Wise Solution of RS Aggarwal including Chapter -22 Trigonometrical Identities RS Aggarwal Goyal Brothersis very help full for ICSE Class 10th student appearing in 2020 exam of council.