万能代换公式
$$
u = \tan \frac{x}{2} \
\sin x = \frac{2u}{1 + u^2} \
\cos x = \frac{1 - u^2}{1 + u^2}
$$
积化和差公式
$$
\sin x \cos y = \frac{1}{2} \left[ \sin (x+y) + \sin (x-y) \right] \
\cos x \sin y = \frac{1}{2} \left[ \sin (x+y) - \sin (x-y) \right] \
\cos x \cos y = \frac{1}{2} \left[ \cos (x+y) + \cos (x-y) \right] \
\sin x \sin y = \frac{1}{2} \left[ \cos (x-y) - \cos (x+y) \right]
$$
