NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry

Learning Mathematics can become a fun-filled journey when students refer to all the solutions from NCERT Solutions for CBSE Class 10 Maths on TopperLearning. NCERT Solutions for CBSE Class 10 Maths come in handy for a quick round of revision, and can be accessed at any time on the portal. TopperLearning's CBSE Class 10 Maths study material comprises the following items, assuring a wholesome kit for perfect preparation: 

       CBSE Class 10 Maths Video Lessons

       CBSE Class 10 Maths sample papers

       CBSE Class 10 Maths Undoubt

       CBSE Class 10 Maths Most Important Questions

       CBSE Class 10 Maths Past Year Papers

       CBSE Class 10 Maths Textbook Solutions

       CBSE Class 10 Maths Revision Notes   

TopperLearning experts leave no stone unturned when it comes to helping students boost their scores. So why wait? Increase your confidence by studying Maths using NCERT solutions for CBSE Class 10 Maths from TopperLearning. 

NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry 

The study of relationships between the sides and angles of triangles is crucial while mastering Trigonometry.  This branch of Mathematics has been included as a very scoring chapter in CBSE Class 10 Maths. It has practical applications and it helps in finding out details with minimal information. The basics taught in this Class 10 Maths chapter Introduction to Trigonometry will interest the students greatly. It is easily comprehensible with TopperLearning’s Maths NCERT solutions for CBSE Class 10. The material created by experts makes studying trigonometry simpler with stepwise solutions and conceptual insights with every question. Video Solutions help you understand the theorems and identities.  The key points discussed in this chapter are.

       Trigonometric Ratios

       Use of Trigonometric Ratios

       Trigonometric Ratios of Some Specific Angles

       Trigonometric Ratios of Complementary Angles

       Trigonometric Identities

While learning these topics, one will need assistance and TopperLearning's study material suffices for all study and exam prep needs. Introduction to Trigonometry NCERT solutions by experts give you stepwise solutions for each and every question from the exercises. 

Mathematics Chapter 8 Introduction to Trigonometry Exercise 8.1 

Learn what the trigonometric ratios are and find the values of all the trigonometric ratios using the given information. Remember, the trigonometric concepts from these chapter will be helpful even in the higher grades. The CBSE Class 10 Maths Textbook solutions by TopperLearning are stepwise solutions written taking in account accuracy and reasoning. Students can tally their solutions and use CBSE Class 10 Maths, or  use the Undoubt feature in case of doubts. Our CBSE Class 10 Maths study material plays a crucial role in helping you understand all key concepts for Class 10 Maths chapter Introduction to Trigonometry. As this is a new chapter, students can often be puzzled when solving the exercises.  TopperLearning’s CBSE Class 10 Maths video lessons can come in handy to clear all your confusion. Once you have solved the exercise, you can attempt the CBSE Class 10 Maths most important questions and CBSE Class 10 Maths sample papers to test your knowledge.

 Mathematics Chapter 8 Introduction to Trigonometry Exercise 8.2 

In this exercise, we will find trigonometric values for some specific angles namely 0,30,45,60,90. Learn the perfect method to memorize the values for every trigonometric ratio for these angles with TopperLearning’s study material. Understand the logical reason for each value by watching our video solutions. Apply your understanding of different types of angles to find the values in the questions asked. TopperLearning’s Introduction to Trigonometry NCERT solutions are written using the method prescribed by the CBSE board.

 Mathematics Chapter 8 Introduction to Trigonometry Exercise 8.3 

Dive in deep and learn Trigonometric Ratios of Complementary Angles with Introduction to Trigonometry NCERT solutions. As you know, formulae make it easier to solve complex problems. With TopperLearning’s study material, you can understand the detailed logic behind applying different formulae to find the values of complementary angles in this CBSE Class 10 Maths exercise. Understand the theorem and its application by watching our video solutions. The solutions have all the calculations and reasoning that need to be mentioned in Introduction to Trigonometry NCERT solutions. 

Mathematics Chapter 8 Introduction to Trigonometry Exercise 8.4

An equation involving trigonometric ratios of an angle is called a trigonometric identity. In the Mathematics chapter Introduction to Trigonometry, we will prove one trigonometric identity, and use it to prove other trigonometric identities in the Maths chapter Introduction to Trigonometry. Understand these identities in the most comprehensive manner with TopperLearning’s CBSE Class 10 Maths video lessons. The class 10 Maths chapter Introduction to Trigonometry is very scoring and hence, students are advised to go through CBSE Class 10 Maths sample papers, CBSE Class 10 Maths most important questions, CBSE Class 10 Maths past year papers and CBSE Class 10 Maths revision notes on our study portal. In case of doubts, you can refer to CBSE Class 10 Maths Doubt Solver and CBSE Class 10 Maths Undoubt portal.

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Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.1

Solution 1

In ABC by applying Pythagoras theorem
AC2 = AB2 + BC2
      = (24)2 + (7)2
      = 576 + 49
      = 625
AC =  = 25 cm





cos space straight C space equals space fraction numerator Side space adjacent space to space angle straight C over denominator hypotenuse end fraction space equals space BC over AC equals space 7 over 25

Solution 2
Solution 3
Solution 4
Solution 5
Solution 6

 

Since angleA and angleB are acute angles, then angleC is a right angle.

cos A = cos B .... given

AC/AB = BC/AB

AC = BC

angleB =angleA           .... angles opposite to equal sides are equal in length.





Solution 7
Solution 8
Solution 9
Solution 10
Solution 11

Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.2

Solution 1
Solution 2


Solution 3
Solution 4

Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.3

Solution 1
Solution 2

Solution 3

Given that

tan 2A = cot (A - 18)

cot (90 - 2A) = cot (A -18)
90 - 2A = A - 18
108 = 3A
A = 36

Solution 4

Given that
tan A = cot B
tan A = tan (90 - B)
A = 90 - B
A + B = 90

Solution 5

Given that
Sec 4A = cosec (A - 20)
Cosec (90 - 4A) = cosec (A - 20)
90 - 4A = A - 20
110 = 5A
A = 22

Solution 6
Solution 7

sin 67 + cos 75
= sin (90 - 23) + cos (90 - 15)
= cos 23 + sin 15

Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.4

Solution 1
We know that
Solution 2
We know that

Solution 3
Solution 4

(i) 9sec2A - 9tan2A
= 9(sec2A - tan2A)
= 9 (1)            (as sec2A - tan2A = 1)
= 9
Hence alternative (B) is correct.

(ii) (1 + tanθ + secθ) (1 + cotθ - cosecθ)

Hence alternative (C) is correct.


(iii) (secA + tanA) (1 - sinA)


(iv)

Solution 5