NCERT Solutions for Maths Class 12 Exercise 2.2

# NCERT Solutions for Maths Class 12 Exercise 2.2

## NCERT Solutions for Maths Class 12 Exercise 2.2

### Maths Class 12 Ex 2.2 Question 1.

Prove the following.

Solution:
Let sin-1 x = Î¸
sin Î¸ = x

R.H.S. = sin-1 (3x – 4x³)
= sin-1 (3 sin Î¸ – 4 sin³ Î¸)
= sin-1 (sin 3Î¸)                                        [
Since, sin 3Î¸ = 3 sin Î¸ – 4 sin³ Î¸]
= 3Î¸
= 3 sin-1 x
= L.H.S.

### Maths Class 12 Ex 2.2 Question 2.

Prove the following.

Solution:

Let cos-1 x = Î¸
x = cos Î¸
R.H.S. = cos-1 (4x³ – 3x)
= cos-1 (4 cos³Î¸ – 3 cos Î¸)
= cos-1 (cos 3Î¸)                                        [
cos 3Î¸ = 4 cos³ Î¸ – 3 cos Î¸]
= 3Î¸
= 3 cos-1 x
= L.H.S.

### Maths Class 12 Ex 2.2 Question 3.

Write the following function in the simplest form.

Solution:
Putting x = tan Î¸, we get Î¸ = tan-1 x.

### Maths Class 12 Ex 2.2 Question 4.

Write the following function in the simplest form.

Solution:

### Maths Class 12 Ex 2.2 Question 5.

Write the following function in the simplest form.

Solution:
Dividing both numerator and denominator by cos x, we get

### Maths Class 12 Ex 2.2 Question 6.

Write the following function in the simplest form.

Solution:
Putting x = a sin Î¸, we get x/a = sin Î¸.

### Maths Class 12 Ex 2.2 Question 7.

Write the following function in the simplest form.
, a > 0; –a/√3 < x < a/√3

Solution:
Putting x = a tan Î¸, we get

### Maths Class 12 Ex 2.2 Question 8.

Find the value of the following.

Solution:

### Maths Class 12 Ex 2.2 Question 9.

Find the value of the following.

Solution:
Putting x = tan Î¸, we get tan-1 x = Î¸.

### Maths Class 12 Ex 2.2 Question 10.

Find the value of the following expression.

Solution:

### Maths Class 12 Ex 2.2 Question 11.

Find the value of the following expression.

Solution:

### Maths Class 12 Ex 2.2 Question 12.

Find the value of the following expression.

Solution:
Let sin-1 3/5 = Î¸, then sin Î¸ = 3/5.

is equal to
(A) 7Ï€/6
(B) 5Ï€/6
(C) Ï€/3
(D) Ï€/6

Solution:

### Maths Class 12 Ex 2.2 Question 14.

is equal to
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1

Solution:

Hence, option (d) is correct.

is equal to
(A) Ï€
(B) –Ï€/2

(C) 0
(D) 2√3

Solution: