Question

This is 12th math question please help me and solve this i am waiting for your answer. This is inverse trigonometric.. Please help me ​

Answer 1

Step-by-step explanation:

Let us consider

$y = \tan^{ - 1} ( \frac{2x}{1 - {x}^{2} } )$

$Putting \: x = \tan(\alpha)$

$\implies \: \alpha = \tan^{-1}(x)$

$y = \tan^{ - 1} ( \frac{2 \tan( \alpha ) }{1 - \tan^{2} ( \alpha ) } )$

$\implies \: y = \tan ^{ - 1} ( \tan( 2\alpha ) )$

$\implies \: y = 2 \alpha$

$\implies \: y = 2 \tan^{ - 1} (x)$

Hence, proved