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) $\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$
$\Rightarrow \tan ^{-1}(1+x)=\frac{\pi}{2}-\tan ^{-1}(1-x)$
$\Rightarrow \tan ^{-1}(1+x)=\cot ^{-1}(1-x)$
$\Rightarrow \tan ^{-1}(1+x)=\tan ^{-1}\left(\frac{1}{1-x}\right)$
$\Rightarrow 1+x=\frac{1}{1-x} \Rightarrow 1-x^2=1 \Rightarrow x=0$

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