Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If x ∈ 
, then value of the expression sin –1 (cos –1 (cos x) + sin –1 (sin x))), is equal to
Text Solution
Verified by ExpertsThe correct answer is:
C
For x ∈ 
, cos –1 (cos x)
= cos –1 (cos (2 π – (2 π – x)))
= cos –1 (cos (2 π – x)) = 2 π – x
and sin –1 (sin x) = sin –1 (sin (2 π + (x – 2 π )))
= x – 2 π
⇒ cos –1 (cos x) + sin –1 (sin x)
= (2 π – x) + (x – 2 π ) = 0.
Therefore
sin –1 (cos(cos –1 (cos x) + sin –1 (sin x))) = sin –1 0 = 0
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