Question:
Find the principal value of each of the following :
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$
Solution:
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{\pi}{3}\right)\right)$
[ Formula: $\sin (\pi-x)=\sin x$ )
$=\sin ^{-1}\left(\sin \frac{\pi}{3}\right)$
[ Formula: $\sin ^{-1}(\sin x)=x$ ]
$=\frac{\pi}{3}$
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