Q. $\sin^{- 1}{x + \sin^{- 1}{\frac{1}{x} + \cos^{- 1}{x + \cos^{- 1}\frac{1}{x}}}}$ is equal to
A) $\pi$
B) $\frac{\pi}{2}$
C) $\frac{3\pi}{2}$
D) None of these
Explanation
(a)
$\sin^{- 1}{x + \sin^{- 1}{\frac{1}{x} + \cos^{- 1}{x + \cos^{- 1}\frac{1}{x}}}}$
$= \lbrack\sin^{- 1}{x + \cos^{- 1}{x\rbrack + \left\lbrack \sin^{- 1}\ \left( \frac{1}{x} \right) + \cos^{- 1}\ \left( \frac{1}{x} \right) \right\rbrack}}$
$= \frac{\pi}{2} + \frac{\pi}{2} = \pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.