Negative argument properties for JEE

Formula

\(\sin^{-1}(-x)=-\sin^{-1}x,\quad \cos^{-1}(-x)=\pi-\cos^{-1}x,\quad \tan^{-1}(-x)=-\tan^{-1}x,\quad \cot^{-1}(-x)=\pi-\cot^{-1}x\)

Variables: \(x\) in the domain of corresponding inverse function.

Conditions: Principal value conventions applied.

Simplification, symmetry, and equation solving.