积化和差

$\sin (\alpha )\cos (\beta )=\frac{1}{2}\left[\sin (\alpha +\beta )+\sin (\alpha -\beta )\right]=-\frac{1}{2}\left[\cos (\alpha +\beta )-\sin (\alpha -\beta )\right]$
$\cos (\alpha )\cos (\beta )=\frac{1}{2}\left[\sin (\alpha +\beta )-\sin (\alpha -\beta )\right]=\frac{1}{2}\left[\cos (\alpha +\beta )+\cos (\alpha -\beta )\right]$