General principal value reduction for \(\tan^{-1}(\tan x)\) for JEE

Formula

\(\tan^{-1}(\tan x)=x-n\pi\) where \(x\in\left(n\pi-\dfrac{\pi}{2},\ n\pi+\dfrac{\pi}{2}\right),\ n\in\mathbb{Z}\)

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

Conditions: Output in \((-\pi/2,\pi/2)\).

Exact evaluation and periodic adjustment problems.