# Trigonometric identities of double angles

$sin2\alpha =2sin\alpha ·cos\alpha =\frac{2tg\alpha }{1+t{g}^{2}\alpha }$
$cos2\alpha =co{s}^{2}\alpha -si{n}^{2}\alpha =\frac{1-t{g}^{2}\alpha }{1+t{g}^{2}\alpha }$
$tg2\alpha =\frac{2tg\alpha }{1-t{g}^{2}\alpha }$
$ctg2\alpha =\frac{ct{g}^{2}\alpha -1}{2ctg\alpha }$
Keywords: trigonometric identities of double angles