( 3 - ^ -1 (-1 2 ) ) is equal to 1. 1 2 2. 1 3 3. 1 4 4. 1 - Vidyadip

Question

$\sin\bigg(\frac{\pi}{3}-\sin^{-1}(-\frac{1}{2})\bigg)$ is equal to

$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{4}$
1

✓

Answer

$\sin^{-1}\bigg(-\frac{1}{2}\bigg)=\sin^{-1}\bigg(-\sin\frac{\pi}{6}\bigg)$
$=\sin^{-1}\bigg[\sin\bigg(-\frac{\pi}{6}\bigg)\bigg]=-\frac{\pi}{6}$
$\therefore\sin\left[\frac{\pi}{3}-\sin^{-1}\left(-\frac{1}{2}\right)\right]=\sin\left[\frac{\pi}{3}-\left(-\frac{\pi}{6}\right)\right]$
$=\sin\left[\frac{\pi}{3}+\frac{\pi}{6}\right]=\sin\frac{3\pi}{6}=\sin\frac{\pi}{2}=1 $
Therefore, option (d) is correct.

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