Expressions for tangent forms from inverse sine and cosine for JEE

Formula

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

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

Conditions: For second formula, \(x\neq 0\); sign follows principal range of \(\cos^{-1}x\).

Conversion of inverse-trig expressions to algebraic form.