The value of ^ -1 ( 53 5 ) is - Vidyadip

MCQ

The value of $\sin ^{-1}\left(\cos \frac{53 \pi}{5}\right)$ is

A
$\frac{-3 \pi}{5}$
✓
$\frac{-\pi}{10}$
C
$\frac{3 \pi}{5}$
D
$\frac{\pi}{10}$

✓

Answer

Correct option: B.

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

(B) $\cos \frac{53 \pi}{5}=\cos \left(\frac{50 \pi}{5}+\frac{3 \pi}{5}\right)$
$=\cos \left(10 \pi+\frac{3 \pi}{5}\right)$
$=\cos \frac{3 \pi}{5}$
$=\sin \left(\frac{\pi}{2}-\frac{3 \pi}{5}\right)=\sin \left(\frac{-\pi}{10}\right)$
$\therefore \quad \sin ^{-1}\left(\cos \frac{53 \pi}{5}\right)=\sin ^{-1}\left(\sin \frac{-\pi}{10}\right)=\frac{-\pi}{10}$

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