Q. If $\sin^{- 1}{= \frac{\pi}{5}}$, for some $x \in ( - 1,\ 1)$, then the value of $\cos^{- 1}x$ is
A) $\frac{3\pi}{10}$
B) $\frac{5\pi}{10}$
C) $\frac{7\pi}{10}$
D) $\frac{9\pi}{10}$
Explanation
(a)
We know, $\sin^{- 1}{x + \cos^{- 1}{x = \frac{\pi}{2}}}$
$\Rightarrow \ \ \cos^{- 1}{x = \frac{\pi}{2} - \sin^{- 1}{x = \frac{\pi}{2} - \frac{\pi}{5}}}$
$\Rightarrow \ \ \cos^{- 1}{x = \frac{3\pi}{10}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.