Expressions for \(\sin(\cos^{-1}x)\) and \(\cos(\sin^{-1}x)\) for JEE

Formula

\(\sin(\cos^{-1}x)=\sqrt{1-x^2},\quad \cos(\sin^{-1}x)=\sqrt{1-x^2}\)

Variables: \(x\in[-1,1]\).

Conditions: Positive square root taken due to principal ranges.

Simplification of inverse-trig compositions.