Rational Functions of Sine/Cosine

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Substitute $$ t = \tan \frac{x}{2} $$ (Weierstrass):
$$ \sin x = \frac{2t}{1+t^2}, \quad \cos x = \frac{1-t^2}{1+t^2}, \quad dx = \frac{2 \, dt}{1+t^2} $$
Converts to rational function in $$ t $$
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