Mathematics · essential
Reverse compositions with principal values for JEE
Inverse trigonometrical functions and their properties
Formula
\(\sin^{-1}(\sin x)=x\) for \(x\in\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right],\quad \cos^{-1}(\cos x)=x\) for \(x\in[0,\pi],\quad \tan^{-1}(\tan x)=x\) for \(x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)\)
Variables: \(x\in\mathbb{R}\).
Conditions: Only valid on principal value intervals.
Handling compositions carefully in JEE problems.