# NCERT Solutions for Exercise 8.3 Class 10 Maths Chapter 8 - Introduction to Trigonometry

NCERT Solutions for Class 10 Maths exercise 8.3- This exercise gives a brief overview of the trigonometric ratios of complementary angles and is explained in trigonometry. If the sum of two angles equals 90°, they are said to be complementary. According to the angle sum property, one angle in a right-angled triangle measures 90°, and the sum of the other two angles also measures 90°. This is the concept from which the formulas for this exercise are derived or the formula of complementary angle. The majority of these questions require proof. As a result, students must carefully study the theory in order to provide detailed answers to these sums.

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In Class 10 Maths NCERT book exercise 8.3, we will see the proof of complementary angles. For finding the complementary angles we should be familiar with are trigonometric ratio and their values.

Along with NCERT syllabus Class 10 Maths chapter 8 exercise 8.3 the following exercises are also present.

Introduction to Trigonometry Exercise 8.1

Introduction to Trigonometry Exercise 8.2

Introduction to Trigonometry Exercise 8.4

**Introduction to Trigonometry**** class 10 chapter 8 ****Exercise: 8.3 ** ** **

** Q1 ** Evaluate :

** Answer: **

We can write the above equation as;

By using the identity of

Therefore,

So, the answer is 1.

** Q1 ** Evaluate :

** Answer: **

The above equation can be written as ;

.........(i)

It is known that,

Therefore, equation (i) becomes,

So, the answer is 1.

** Q1 ** Evaluate :

** Answer: **

The above equation can be written as ;

....................(i)

It is known that

Therefore, equation (i) becomes,

So, the answer is 0.

** Q1 ** Evaluate :

** Answer: **

This equation can be written as;

.................(i)

We know that

Therefore, equation (i) becomes;

= 0

So, the answer is 0.

** Q2 ** Show that :

** Answer: **

Taking Left Hand Side (LHS)

=

[it is known that and

Hence proved.

** Q2 ** Show that :

** Answer: **

Taking Left Hand Side (LHS)

=

=

= [it is known that and ]

= 0

** Q3 ** If , where is an acute angle, find the value of .

** Answer: **

We have,

2A = (A - )

we know that,

** Q4 ** If , prove that .

** Answer: **

We have,

and we know that

therefore,

A = 90 - B

A + B = 90

Hence proved.

** Q5 ** If , where is an acute angle, find the value of .

** Answer: **

We have,

, Here 4A is an acute angle

According to question,

We know that

** Q6 ** If and are interior angles of a triangle , then show that

** Answer: **

Given that,

A, B and C are interior angles of

To prove -

Now,

In triangle ,

A + B + C =

Hence proved.

** Q7 ** Express in terms of trigonometric ratios of angles between and .

** Answer: **

By using the identity of and

We know that,

and

the above equation can be written as;

**More About NCERT Solutions for Class 10 Maths Exercise 8.3**

NCERT solutions for Class 10 Maths exercise 8.3- We can find the value of these complementary angles but in the examination, we have very little time. So, we should try to remember these formulas NCERT solutions for Class 10 Maths chapter 8 exercise 8.3 as these can break a large complex trigonometric equation into simpler ones that can be called easily by the other associated terms present in the function.

The formulas are:

,

,

,

,

,

for all values of angle, A lying between 0° and 90°.

We should always be careful about

and

are not defined.

**Also Read| **Introduction to Trigonometry Class 10 Notes

**Benefits of NCERT Solutions for Class 10 Maths Exercise 8.3**

Exercise 8.3 Class 10 Maths, is based on the main concept of Trigonometric Ratios of Complementary Angles.

Class 10 Maths chapter 8 exercise 8.3 helps in solving and revising all questions of the previous exercises. It shows us two different aspects of solving the same problem by using complementary angels.

Mastering the complementary angle formulas of Class 10 Maths chapter 8 exercise 8.3 can help in simplifying complex trigonometric questions into simpler ones.

**Also see-**

- NCERT Exemplar Solutions Class 10 Maths Chapter 8
- NCERT Solutions for Class 10 Maths Chapter 8

**NCERT Solutions Subject Wise**

- NCERT Solutions Class 10 Science
- NCERT Solutions for Class 10 Maths

**Subject wise NCERT Exemplar solutions**

- NCERT Exemplar Class 10 Maths
- NCERT Exemplar Class 10 Science