Q. If $4\sin^{- 1}{x + \cos^{- 1}{x = \pi},\ \ }$ then $x$ is equal to
A) 0
B) 1/2
C) -1/2
D) 1
Explanation
(b)
Given, $4\sin^{- 1}{x + \cos^{- 1}{x = \pi}}$
$\Rightarrow \ 4\sin^{- 1}{x + \frac{\pi}{2} - \sin^{- 1}{x = \pi}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\sin^{- 1}{x = \frac{\pi}{2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin^{- 1}{x = \frac{\pi}{6}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.