The value of ^ -1 ( 13 5 ) is - Vidyadip

MCQ

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

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

✓

Answer

Correct option: B.

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

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

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