Find the value of ^ -1 ( 3 5 ). - Vidyadip

Question

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

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Answer

$
\begin{aligned}
\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right) & =\sin ^{-1}\left[\cos \left(6 \pi+\frac{3 \pi}{5}\right)\right] \\
& =\sin ^{-1}\left[\cos \frac{3 \pi}{5}\right] \\
& =\sin ^{-1}\left[\sin \left(\frac{\pi}{2}-\frac{3 \pi}{5}\right)\right] \\
& =\sin ^{-1}\left[\sin \left(\frac{-\pi}{10}\right)\right] \\
& =\frac{-\pi}{10} \text { }
\end{aligned}
$

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