The value of ^ -1 ( 13 5 ) is

Question

The value of $\sin ^{-1}\left(\cos \frac{13 \pi}{5}\right)$ is

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Answer

$\text {We have, } \sin ^{-1}\left(\cos \frac{13 \pi}{5}\right)=\sin ^{-1}\left[\cos \left(2 \pi+\frac{3 \pi}{5}\right)\right]$
$=\sin ^{-1}\left[\cos \frac{3 \pi}{5}\right]=\sin ^{-1}\left[\cos \left(\frac{\pi}{2}+\frac{\pi}{10}\right)\right]$
$=\sin ^{-1}\left(-\sin \frac{\pi}{10}\right)=-\sin ^{-1}\left(\sin \frac{\pi}{10}\right)=-\frac{\pi}{10}$

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