Weierstrass Substitution

Rarely Tested

Weierstrass Substitution

For trigonometric rational functions, put:

$$t=\tan\frac{x}{2}$$

then:

$$\sin x=\frac{2t}{1+t^2}$$

and:

$$\cos x=\frac{1-t^2}{1+t^2}$$

Usage

- Used to convert rational functions of $$\sin x$$ and $$\cos x$$ into rational functions of $$t$$.

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