If 4 ^ - 1 x + ^ - 1 x = , then x is equal to - Vidyadip

MCQ

If $4{\sin ^{ - 1}}x + {\cos ^{ - 1}}x = \pi ,$ then $x$ is equal to

A
$0$
✓
$\frac{1}{2}$
C
$ - \frac{{\sqrt 3 }}{2}$
D
$\frac{1}{{\sqrt 2 }}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

b
(b) We know that $4{\sin ^{ - 1}}x + {\cos ^{ - 1}}x = \pi $

==> $3{\sin ^{ - 1}}x + {\sin ^{ - 1}}x + {\cos ^{ - 1}}x = \pi $

==> $3{\sin ^{ - 1}}x = \pi - \frac{\pi }{2} = \frac{\pi }{2}$

==> ${\sin ^{ - 1}}x = \pi /6$

==> $x = \sin \frac{\pi }{6} = \frac{1}{2}$.

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