## Book: RD Sharma - Mathematics (Volume 1)

### Chapter: 4. Inverse Trigonometric Functions

#### Subject: Maths - Class 12th

##### Q. No. 28 of MCQ

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

28
##### Choose the correct answerThe value of is

We need to find the value of

Let

Now, take sine on both sides,

Using the property of inverse trigonometry,

sin(sin-1 A) = A

Let us find the value of cos x.

We know by trigonometric identity, that

sin2 x + cos2 x = 1

cos2 x = 1 – sin2 x

Put the value of sin x,

We have,

…(i)

Using the trigonometric identity,

cos 2x = cos2 x – sin2 x

cos 2x = (1 – sin2x) – sin2 x [, sin2 x + cos2 x = 1]

cos 2x = 1 – sin2 x – sin2 x

cos 2x = 1 – 2 sin2 x

Or,

2 sin2 x = 1 – cos 2x

Replacing x by x/4,

Substituting the value of in equation (i),

…(ii)

Using the trigonometric identity,

cos 2x = cos2 x – sin2 x

cos 2x = cos2 x – (1 – cos2 x) [, sin2 x + cos2 x = 1]

cos 2x = cos2 x – 1 + cos2x

cos 2x = 2 cos2 x – 1

Or,

2 cos2 x = 1 + cos 2x

Replacing x by x/2,

Substituting the value of in equation (ii),

Put the value of cos x as found above, cos x = 1/8.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35