## NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions Miscellaneous Exercise

#### Page No 51:

#### Question 1:

Find the value of

#### Answer:

We know that cos

^{−1}(cos*x*) =*x*if, which is the principal value branch of cos^{−1}*x*.
Here,

Now, can be written as:

#### Question 2:

Find the value of

#### Answer:

We know that tan

^{−1}(tan*x*) =*x*if, which is the principal value branch of tan^{−1}*x*.
Here,

Now,

can be written as:

#### Question 3:

Prove

#### Answer:

Now, we have:

#### Question 4:

Prove

#### Answer:

Now, we have:

#### Question 5:

Prove

#### Answer:

Now, we will prove that:

#### Question 6:

Prove

#### Answer:

Now, we have:

#### Question 7:

Prove

#### Answer:

Using (1) and (2), we have

#### Question 8:

Prove

#### Answer:

#### Page No 52:

#### Question 9:

Prove

#### Answer:

#### Question 10:

Prove

#### Answer:

#### Question 11:

Prove [

**Hint:**put*x*= cos 2*θ*]#### Answer:

#### Question 12:

Prove

#### Answer:

#### Question 13:

Solve

#### Answer:

#### Question 14:

Solve

#### Answer:

#### Question 15:

Solveis equal to

**(A)**(

**B)**(

**C)**(

**D)**

#### Answer:

Let tan

^{−1}*x*=*y*. Then,
The correct answer is D.

#### Question 16:

Solve

**,**then*x*is equal to**(**

**A)**(

**B)**(

**C)**0 (

**D)**

#### Answer:

Therefore, from equation (1), we have

Put

*x*= sin*y*. Then, we have:
But, when, it can be observed that:

is not the solution of the given equation.

Thus,

*x*= 0.
Hence, the correct answer is

**C**.#### Question 17:

Solveis equal to

**(A)**

**(B).**

**(C)**

**(D)**

#### Answer:

Hence, the correct answer is

**C**._{}

^{}