# NCERT Solutions for Exercise 8.4 Class 10 Maths Chapter 8 - Introduction to Trigonometry

NCERT Solutions for Class 10 Maths exercise 8.4- This exercise is one of the most important exercises in trigonometry both for exam and for aptitude. When an equation holds true for all possible values of the variables, it is referred to as an identity.

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Similarly, a trigonometric identity is an equation involving trigonometric ratios of an angle that holds true for all values of the angle(s).

NCERT solutions Class 10 Maths exercise 8.4 – we all know about the Pythagoras Theorem. It states that if a triangle is right-angled (90 degrees), the square of the hypotenuse equals the sum of the squares of the other two sides, that is , where AB denotes the base, AC denotes the altitude or height, and BC denotes the hypotenuse.

We can prove every formula using this Pythagoras theorem. We have to understand the derivation of these formulas. From an examination point of view, we should remember them.

Along with NCERT book Class 10 Maths chapter 8 exercise 8.4, the following exercises are also present.

Introduction to Trigonometry Exercise 8.1

Introduction to Trigonometry Exercise 8.2

Introduction to Trigonometry Exercise 8.3

**Introduction to Trigonometry**** Class 10 Chapter 8 ****Exercise: 8.4 **

** Q1 ** Express the trigonometric ratios and in terms of .

** Answer: **

We know that

(i)

(ii) We know the identity of

(iii)

** Q2 ** Write all the other trigonometric ratios of in terms of .

** Answer: **

We know that the identity

** Q3 ** Evaluate :

** Answer: **

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

The above equation can be written as;

(Since )

** Q3 ** Evaluate :

** Answer: **

** We know that **

** Therefore, **

** Q4 ** Choose the correct option. Justify your choice.

(A) 1 (B) 9 (C) 8 (D) 0

** Answer: **

The correct option is (B) = 9

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

and it is known that sec^{2}A-tan^{2}A=1

Therefore, equation (i) becomes,

** Q4 ** Choose the correct option. Justify your choice.

(A) 0 (B) 1 (C) 2 (D) –1

** Answer: **

The correct option is (C)

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

we can write his above equation as;

= 2

** Q4 ** Choose the correct option. Justify your choice.

** Answer: **

The correct option is (D)

** Q4 ** Choose the correct option. Justify your choice.

** Answer: **

The correct option is (D)

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

The above equation can be written as;

We know that

therefore,

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

We need to prove-

Now, taking LHS,

LHS = RHS

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

We need to prove-

taking LHS;

= RHS

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

[ ** Hint**: Write the expression in terms of and ]

** Answer: **

We need to prove-

Taking LHS;

By using the identity a ^{ 3 } - b ^{ 3 } =(a - b) (a ^{ 2 } + b ^{ 2 } +ab)

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

[ ** Hint ** : Simplify LHS and RHS separately]

### Answer:

We need to prove-

taking LHS;

Taking RHS;

We know that identity

LHS = RHS

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined. , using the identity

** Answer: **

We need to prove -

Dividing the numerator and denominator by , we get;

Hence Proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

We need to prove -

Taking LHS;

By rationalising the denominator, we get;

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

We need to prove -

Taking LHS;

[we know the identity ]

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

Given equation,

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

Taking LHS;

[since ]

Hence proved

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

[ ** Hint ** : Simplify LHS and RHS separately]

** Answer: **

We need to prove-

Taking LHS;

Taking RHS;

LHS = RHS

Hence proved.

** Q5 ** Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

** Answer: **

We need to prove,

Taking LHS;

Taking RHS;

LHS = RHS

Hence proved.

**More About NCERT Solutions for Class 10 Maths Exercise 8.4**

NCERT solutions for Class 10 Maths exercise 8.4- We will try to derive an important formula from NCERT solutions for Class 10 Maths chapter 8 exercise 8.4 by applying the Pythagoras theorem to it. And the Pythagoras Theorem states that the sum of the squares of the base and the perpendicular is equal to the square of the hypotenuse.

.

We will divide the whole equation by

And we know that sin is the ratio of perpendicular and hypotenuse while cos is the ratio of base and hypotenuse.

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

The other formulas that have similar use as the above are:

and

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

**Benefits of NCERT Solutions for Class 10 Maths Exercise 8.4**

Exercise 8.4 Class 10 Maths, is based on the main concept of Trigonometric Identities.

NCERT syllabus Class 10 Maths chapter 8 exercise 8.4 helps in solving and revising all questions of these exercises.

Mastering the values of these trigonometric identities of Class 10 Maths chapter 8 exercise 8.4 can help in simplifying complex trigonometric questions into simpler ones and proving different equations of physics in later higher classes.

**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