Write the value

Question:

Write the value of $\sin ^{-1}\left(\sin \frac{3 \pi}{5}\right)$

Solution:

$\sin ^{-1}\left(\sin \frac{3 \pi}{5}\right)=\sin ^{-1}\left[\sin \left(\pi-\frac{2 \pi}{5}\right)\right]$

$=\sin ^{-1}\left(\sin \frac{2 \pi}{5}\right)$

$=\frac{2 \pi}{5}$

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