If $ - 1 < x < 1$, then ${\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)$ equals

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

- 1 < x < 1

, then

{\tan ^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)

equals

View answer and explanation

Correct option: A

2{\tan ^{ - 1}}x

Option A (

2{\tan ^{ - 1}}x

) is correct because using the identity

\tan 2\theta = \frac{{2\tan \theta}}{{1 - {{\tan }^2}\theta}}

and the given condition

-1 < x < 1

, we can simplify the expression.

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x

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