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Question

Question: If \(\sin ^ { - 1 } ( \sin x )\)is equal to....

If sin⁡−1(sin⁡x)\sin ^ { - 1 } ( \sin x )is equal to.

A

x

B

−x- x

C

π+x\pi + x

D

π−x\pi - x

Answer

π−x\pi - x

Explanation

Solution

We have π2≤x≤3π2\frac { \pi } { 2 } \leq x \leq \frac { 3 \pi } { 2 }

⇒−π2≤x−π≤π2⇒−π2≤π−x≤π2\Rightarrow \frac { - \pi } { 2 } \leq x - \pi \leq \frac { \pi } { 2 } \Rightarrow \frac { - \pi } { 2 } \leq \pi - x \leq \frac { \pi } { 2 }

⇒sin⁡−1{sin⁡(π−x)}=π−x\Rightarrow \sin ^ { - 1 } \{ \sin ( \pi - x ) \} = \pi - x.