[ 3 + ^ -1 (1 2 ) ] is equal to - Vidyadip

Question

$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$ is equal to

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Answer

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

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