Question

If $4co{s}^{-1}x+si{n}^{-1}x=\pi$, 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, $4co{s}^{-1}x+si{n}^{-1}x=\pi$
$\Rightarrow 4\left\{\frac{\pi }{2}-si{n}^{-1}x\right\}+si{n}^{-1}x=\pi$
$\Rightarrow 2\pi -4si{n}^{-1}x+si{n}^{-1}x=\pi$
$\Rightarrow 3si{n}^{-1}x=\pi$
$\Rightarrow si{n}^{-1}x=\frac{\pi }{3}$
$\Rightarrow x=sin\frac{\pi }{3}=\frac{\sqrt{3}}{2}$