Question:
The value of sin-1 cos 33π/5 is
(a) 3π/5
(b) -7π/5
(c) π/10
(d) -π/10
Solution:
(d) -π/10
$\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)=\sin ^{-1}\left(\cos \left(6 \pi+\frac{3 \pi}{5}\right)\right)=\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right)$
$=\sin ^{-1}\left[\sin \left(\frac{\pi}{2}-\frac{3 \pi}{5}\right)\right]$
$=\sin ^{-1}\left(\sin \left(-\frac{\pi}{10}\right)\right)$
$=-\frac{\pi}{10} \quad\left(\because \sin ^{-1}(\sin x)=x\right.$, for $\left.x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\right)$