Question

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

• A. $\frac{3\pi }{5}$
• B. $\frac{3\pi }{5}$
• C. $\frac{\pi }{10}$
• D. $-\frac{\pi }{10}$

Answer 1

The correct option is D $-\frac{\pi }{10}$

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