# Sum and difference of trigonometric functions

$sin\alpha +sin\beta =2sin\frac{\alpha +\beta }{2}·cos\frac{\alpha -\beta }{2}$
$sin\alpha -sin\beta =2cos\frac{\alpha +\beta }{2}·sin\frac{\alpha -\beta }{2}$
$cos\alpha +cos\beta =2cos\frac{\alpha +\beta }{2}·cos\frac{\alpha -\beta }{2}$
$cos\alpha -cos\beta =-2sin\frac{\alpha +\beta }{2}·sin\frac{\alpha -\beta }{2}$
$tg\alpha ±tg\beta =\frac{sin\left(\alpha ±\beta \right)}{cos\alpha ·cos\beta }$
$ctg\alpha +ctg\beta =\frac{sin\left(\alpha +\beta \right)}{sin\alpha ·sin\beta }$
$ctg\alpha -ctg\beta =\frac{sin\left(\beta -\alpha \right)}{sin\alpha ·sin\beta }$
Keywords: sum and difference of trigonometric functions