Tangent half-angle substitution identities for JEE

Formula

\[t=\tan\frac{x}{2},\quad \sin x=\frac{2t}{1+t^2},\quad \cos x=\frac{1-t^2}{1+t^2},\quad dx=\frac{2}{1+t^2}\,dt\]

Variables: \(t\) is the new variable.

Conditions: Useful for rational functions of \(\sin x\) and \(\cos x\).

Universal trigonometric substitution.