Question

Write the value of $\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]$.

Answer 1

SOLUTION :  $\sin \left[\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right]=\sin \left(\frac{\pi}{3}-\sin ^{-1}\left(-\sin \frac{\pi}{6}\right)\right)=\sin \left(\frac{\pi}{3}+\frac{\pi}{6}\right)=\sin \frac{3 \pi}{6}=\sin \frac{\pi}{2}=1$