## NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions Ex 2.1

#### Page No 41:

#### Question 1:

Find the principal value of

#### Answer:

Let sin

^{-1 }Then sin*y*=
We know that the range of the principal value branch of sin

^{−1}is
and sin

Therefore, the principal value of

#### Question 2:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of cos

^{−1}is
.

Therefore, the principal value of.

#### Question 3:

Find the principal value of cosec

^{−1}(2)#### Answer:

Let cosec

^{−1}(2) =*y*. Then,
We know that the range of the principal value branch of cosec

^{−1}is
Therefore, the principal value of

#### Question 4:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of tan

^{−1}is
Therefore, the principal value of

#### Question 5:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of cos

^{−1}is
Therefore, the principal value of

#### Question 6:

Find the principal value of tan

^{−1}(−1)#### Answer:

Let tan

^{−1}(−1) =*y*. Then,
We know that the range of the principal value branch of tan

^{−1}is
Therefore, the principal value of

#### Page No 42:

#### Question 7:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of sec

^{−1}is
Therefore, the principal value of

#### Question 8:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of cot

^{−1}is (0,π) and
Therefore, the principal value of

#### Question 9:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of cos

^{−1}is [0,π] and
.

Therefore, the principal value of

#### Question 10:

Find the principal value of

#### Answer:

We know that the range of the principal value branch of cosec

^{−1}is
Therefore, the principal value of

#### Question 11:

Find the value of

#### Answer:

#### Question 12:

Find the value of

#### Answer:

#### Question 13:

Find the value of if sin

^{−1}*x*=*y*, then**(**

**A)**

**(B)**

**(**

**C)**

**(D)**

#### Answer:

It is given that sin

^{−1}*x*=*y*.
We know that the range of the principal value branch of sin

^{−1}is
Therefore,.

#### Question 14:

Find the value of is equal to

**(**

**A)**π (

**B)**(

**C)**(

**D)**

#### Answer:

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