Q. If $\sin^{- 1}{x + \sin^{- 1}{y = \frac{\pi}{2}}}$, then $\cos^{- 1}{x + \cos^{- 1}y}$ is equal to
A) $\frac{\pi}{2}$
B) $\frac{\pi}{4}$
C) $\pi$
D) $\frac{3\pi}{4}$
Explanation
(a)
Given, $\sin^{- 1}{x + \sin^{- 1}{y = \frac{\pi}{2}}}$
$\therefore\ \ \ \frac{\pi}{2} - \cos^{- 1}{x + \frac{\pi}{2} - \cos^{- 1}{y = \frac{\pi}{2}}}$
$\Rightarrow \ \cos^{- 1}{x + \cos^{- 1}{y = \frac{\pi}{2}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.