The value of

Question:

The value of $\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$ is

(a) $\frac{3 \pi}{5}$

(b) $-\frac{7 \pi}{5}$

(c) $\frac{\pi}{10}$

(d) $-\frac{\pi}{10}$

Solution:

$\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$

$=\sin ^{-1}\left[\cos \left(6 \pi+\frac{3 \pi}{5}\right)\right]$

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

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

$=\sin ^{-1}\left[\sin \left(-\frac{\pi}{10}\right)\right]$

$=-\frac{\pi}{10}$

Thus, the value of $\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$ is $-\frac{\pi}{10}$.

Hence, the correct answer is option (d).

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