First slide

Properties of ITF

Question

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

Moderate

A

$x = 1$
B

$x = - 1$
C

$x = 0$
D

$x = π$

Solution

We have,
$\begin{aligned} \tan^{- 1} (1 + x) + \tan^{- 1} (1 - x) = \frac{π}{2} \\ \Rightarrow \tan^{- 1} (1 + x) = \frac{π}{2} - \tan^{- 1} (1 - x) \end{aligned}$
$\begin{array}{l} \Rightarrow \tan^{- 1} (1 + x) = \cot^{1} (1 - x) \\ \Rightarrow \tan^{- 1} (1 + x) = \tan^{- 1} (\frac{1}{1 - x}) \\ \Rightarrow 1 + x = \frac{1}{1 - x} \Rightarrow 1 - x^{2} = 1 \Rightarrow x = 0 \end{array}$

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