If ^ - 1 1 2 = ^ - 1 x, then x = - Vidyadip

MCQ

If ${\sin ^{ - 1}}\frac{1}{2} = {\tan ^{ - 1}}x,$ then $ x =$

A
$\sqrt 3 $
✓
$\frac{1}{{\sqrt 3 }}$
C
$\frac{1}{{\sqrt 2 }}$
D
None of these

✓

Answer

Correct option: B.

$\frac{1}{{\sqrt 3 }}$

b
(b) Given that ${\sin ^{ - 1}}\frac{1}{2} = {\tan ^{ - 1}}x$

$ \Rightarrow \,\,{\tan ^{ - 1}}x = \frac{\pi }{6}$

$ \Rightarrow \,\,x = \tan {30^o} = \frac{1}{{\sqrt 3 }}$.

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