First slide

Properties of ITF

Question

If $x \geq 1,$ then $2 \tan^{- 1} x + \sin^{- 1} (\frac{2 x}{1 + x^{2}})$ is equal to

Moderate

A

$4 \tan^{- 1} x$
B

0
C

$π / 2$
D

$π$

Solution

We have,
$\sin^{- 1} (\frac{2 x}{1 + x^{2}}) = π - 2 \tan^{- 1} x$ for $x \geq 1$
$\begin{aligned} ∴ 2 \tan^{- 1} x + \sin^{- 1} (\frac{2 x}{1 + x^{2}}) \\ = 2 {lan}^{- 1} x + π - 2 \tan^{- 1} x = π \end{aligned}$

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