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Tangent half-angle substitution

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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}}} .

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