Question

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

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

Answer 1

Answer: (C)

$4co{s}^{-1}x+si{n}^{-1}x=\pi$
$\Rightarrow 3co{s}^{-1}x+co{s}^{-1}x+si{n}^{-1}x=\pi$
$\Rightarrow 3co{s}^{-1}x+\frac{\pi }{2}=\pi$
$\Rightarrow 3co{s}^{-1}x=\frac{\pi }{2}$
$\Rightarrow co{s}^{-1}x=\frac{\pi }{6}$
$\Rightarrow x=cos\frac{\pi }{6}$
$=\frac{\sqrt{3}}{2}$