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

MCQ

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

A
$\frac{1}{2}$
B
$\frac{1}{3}$
C
-1
D
1

✓

Answer

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

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