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

MCQ

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

A
$\frac{{2x}}{{\sqrt {1 - {x^2}} }}$
B
$\frac{{2x}}{{1 - {x^2}}}$
✓
$\frac{{2x}}{{1 + {x^2}}}$
D
None of these

✓

Answer

Correct option: C.

$\frac{{2x}}{{1 + {x^2}}}$

c
(c) Given that $A = {\tan ^{ - 1}}x$

Now $x = \tan A \Rightarrow \sin 2A = \frac{{2\tan A}}{{1 + {{\tan }^2}A}} = \frac{{2x}}{{1 + {x^2}}}$.

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