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Tangent half-angle substitution
Change of variable for integrals involving trigonometric functions
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. The general transformation formula is: ∫ f ( sin x , cos x ) d x = ∫ f (...
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