Two-times inverse tangent identity for JEE

Formula

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

Variables: \(x\in\mathbb{R}\).

Conditions: Principal value may require adjustment by \(\pm\pi\) when \(|x|>1\).

Simplifying multiple-angle inverse tangent expressions.