Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 28 of MCQ
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Choose the correct answer
The 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.
