A solution of the equation ^ - 1 (1 + x) + ^ - 1 (1 - x) = 2 is - Vidyadip

MCQ

A solution of the equation ${\tan ^{ - 1}}(1 + x)$ $ + {\tan ^{ - 1}}(1 - x)$ $ = \frac{\pi }{2}$ is

A
$x = 1$
B
$x = - 1$
✓
$x = 0$
D
$x = \pi $

✓

Answer

Correct option: C.

$x = 0$

c
(c) ${\tan ^{ - 1}}(1 + x) + {\tan ^{ - 1}}(1 - x) = \frac{\pi }{2}$

==> ${\tan ^{ - 1}}(1 + x) = \frac{\pi }{2} - {\tan ^{ - 1}}(1 - x)$

==> ${\tan ^{ - 1}}(1 + x) = {\cot ^{ - 1}}(1 - x)$

==> ${\tan ^{ - 1}}(1 + x) = {\tan ^{ - 1}}\left( {\frac{1}{{1 - x}}} \right)$

==> $1 + x = \frac{1}{{1 - x}} \Rightarrow 1 - {x^2} = 1 \Rightarrow x = 0$.

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