Question

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

• A. $\frac{3}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

Answer: (C)

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