Doppelwinkelfunktionen

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