If 3 ^ -1 x + ^ -1 x = then x: - Vidyadip

MCQ

If $ 3\cos ^{ -1 }{ \text{x} } +\sin ^{ -1 }{\text{ x} } =\pi $ then $x:$

A
$\frac { 4 }{ \sqrt { 2 } }$
B
$ -\frac { 1 }{ \sqrt { 2 } }$
✓
$\frac { 1 }{ \sqrt { 2 } }$
D
$\frac { 1 }{ \sqrt { 4 } }$

✓

Answer

Correct option: C.

$\frac { 1 }{ \sqrt { 2 } }$

$ \sin^{-1}\text{x} +\cos^{-1}\text{x}=\frac{\pi}{2}$
$ =3\cos^{-1}\text{x}+\sin^{-1}\text{x}$
$ =2\cos^{1}\text{x}+\cos^{-1}\text{x}+\sin^{-1}\text{x}$
$=\sin^{−1}\text{x}=π$
$ = 2\cos^{-1}\text{x}+\frac{\pi}{2}$
$ =\pi=2\cos^{−1}\text{x}=\frac{\pi}{2}$
$= \cos^{-1}\text{x}=\frac{\pi}{4}\text{x}$
$=\cos (\frac{\pi}{4})=\frac{1}{\sqrt 2}$

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