Trigonometric identities of half angles

$si{n}^{2}\frac{\alpha }{2}=\frac{1-cos\alpha }{2}$
$co{s}^{2}\frac{\alpha }{2}=\frac{1+cos\alpha }{2}$
$tg\frac{\alpha }{2}=\frac{1-cos\alpha }{sin\alpha }=\frac{sin\alpha }{1+cos\alpha }$
$ctg\frac{\alpha }{2}=\frac{1+cos\alpha }{sin\alpha }=\frac{sin\alpha }{1-cos\alpha }$
Keywords: trigonometric identities of half angles