Standard identities of inverse trigonometric functions for JEE

Formula

\[\sin^{-1}x+\cos^{-1}x=\frac\pi2,\qquad \tan^{-1}x+\cot^{-1}x=\frac\pi2\]

Variables: \(x\) real where expressions are defined.

Conditions: First identity for \(x\in[-1,1]\); second for all real \(x\) under principal values.

Simplification in limits and derivatives.