Question

The value of $\sin ^{-1}\left[\cos \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right]$ is

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{6}$
• C. $\frac{-\pi}{3}$
• D. $\frac{-\pi}{6}$

Answer 1

Answer: (B)

Let $\theta =\sin ^{-1}\left[\cos \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right] $
$ =\sin ^{-1}\left[\cos \frac{\pi}{3}\right]\left(\because \text { range of } \sin ^{-1} x \text { is }\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\right) $
$ =\sin ^{-1}\left[\frac{1}{2}\right]=\frac{\pi}{6}$