Tangent half-angle substitution

The tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of x {\textstyle x} into an ordinary rational function of t {\textstyle t} by setting t = tan ⁡ x 2 {\textstyle t=\tan {\tfrac {x}{2}}} . This is the one-dimensional stereographic projection of the unit circle parametrized by angle measure onto the real line.

Source: Wikipedia — Tangent half-angle substitution (CC BY-SA 4.0)