Produkte der Winkelfunktionen

$\displaystyle \sin x \; \sin y$	$\displaystyle =$	$\displaystyle \frac{1}{2}\Big(\cos (x-y) - \cos (x+y)\Big)$
$\displaystyle \cos x \; \cos y$	$\displaystyle =$	$\displaystyle \frac{1}{2}\Big(\cos (x-y) + \cos (x+y)\Big)$
$\displaystyle \sin x \; \cos y$	$\displaystyle =$	$\displaystyle \frac{1}{2}\Big(\sin (x-y) + \sin (x+y)\Big)$
$\displaystyle \cos x \; \sin y$	$\displaystyle =$	$\displaystyle \frac{1}{2}\Big(- \sin (x-y) + \sin (x+y)\Big)$
$\displaystyle \tan x \; \tan y$	$\displaystyle =$	$\displaystyle \frac{\tan x + \tan y}{\cot x + \cot y} = - \frac{\tan x - \tan y}{\cot x - \cot y}$

$\displaystyle \cot x \; \cot y$	$\displaystyle =$	$\displaystyle \frac{\cot x + \cot y}{\tan x + \tan y} = - \frac{\cot x - \cot y}{\tan x - \tan y}$
$\displaystyle \tan x \; \cot y$	$\displaystyle =$	$\displaystyle \frac{\tan x + \cot y}{\cot x + \tan y} = - \frac{\tan x - \cot y}{\cot x - \tan y}$

$\displaystyle \sin x \; \sin y \; \sin z$	$\displaystyle =$	$\displaystyle \frac{1}{4} \Big(\sin (x+y-z) + \sin (y+z-x) + \sin (z+x-y) - \sin (x+y+z)\Big)$
$\displaystyle \cos x \; \cos y \; \cos z$	$\displaystyle =$	$\displaystyle \frac{1}{4} \Big(\cos (x+y-z) + \cos (y+z-x) + \cos (z+x-y) + \cos (x+y+z)\Big)$
$\displaystyle \sin x \; \sin y \; \cos z$	$\displaystyle =$	$\displaystyle \frac{1}{4} \Big(- \cos (x+y-z) + \cos (y+z-x) + \cos (z+x-y) - \cos (x+y+z)\Big)$
$\displaystyle \sin x \; \cos y \; \cos z$	$\displaystyle =$	$\displaystyle \frac{1}{4} \Big(\sin (x+y-z) - \sin (y+z-x) + \sin (z+x-y) + \sin (x+y+z)\Big)$