If 4 ^ -1 x+ ^ -1 x= , then the value of x is: - Vidyadip

MCQ

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

A
$\frac{3}{2}$
B
$\frac{1}{\sqrt2}$
✓
$\frac{\sqrt3}{2}$
D
$\frac{2}{\sqrt3}$

✓

Answer

Correct option: C.

$\frac{\sqrt3}{2}$

We know that $\sin^{-1}\text{x}+\cos^{-1}\text{x}=\frac{\pi}{2}$
$4\cos^{-1}\text{x}+\sin^{-1}\text{x}=\pi$
$\Rightarrow4\cos^{-1}\text{x}+\frac{\pi}{2}-\cos^{-1}\text{x}=\pi $
$\Rightarrow3\cos^{-1}\text{x}=\pi-\frac{\pi}{2}$
$\Rightarrow3\cos^{-1}\text{x}=\frac{\pi}{2}$
$\Rightarrow\cos^{-1}\text{x}=\frac{\pi}{6}$
$\Rightarrow\text{x}=\cos\frac{\pi}{6}$

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