Question

If $4\,\cos^{-1}x+\sin^{-1} x=\pi$, then the value of $x$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt2}$
• C. $\frac{\sqrt3}{2}$
• D. $\frac{2}{\sqrt3}$

Answer 1

Answer: (C)

$4\,cos^{-1} x+sin^{-1} x = \pi$
$\Rightarrow 3\, cos^{-1}x+cos^{-1}x+sin^{-1}x =\pi $
$ \Rightarrow 3\,cos^{-1} x +\frac{\pi}{2} = \pi$
$ \Rightarrow 3 \,cos^{-1}x = \frac{\pi}{2} $
$ \Rightarrow cos^{-1}x = \frac{\pi}{6} $
$ \Rightarrow x=cos \frac{\pi}{6} $
$ = \frac{\sqrt{3}}{2}$