If ^ - 1 x + ^ - 1 ( 1 2 ) = 2 , then x is - Vidyadip

MCQ

If ${\sin ^{ - 1}}x + {\cot ^{ - 1}}\left( {\frac{1}{2}} \right) = \frac{\pi }{2},$ then $x $ is

A
$0$
✓
$\frac{1}{{\sqrt 5 }}$
C
$\frac{2}{{\sqrt 5 }}$
D
$\frac{{\sqrt 3 }}{2}$

✓

Answer

Correct option: B.

$\frac{1}{{\sqrt 5 }}$

b
(b) $\because$ ${\cot ^{ - 1}}\frac{1}{2} = {\cos ^{ - 1}}\frac{1}{{\sqrt 5 }}$

Hence given equation can be written as

${\sin ^{ - 1}}x + {\cos ^{ - 1}}\frac{1}{{\sqrt 5 }} = \frac{\pi }{2}$

$ \Rightarrow $ $x = \frac{1}{{\sqrt 5 }}$.

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