Question

Докажите тождество:

$frac{sin2a+sin2b}{cos2a+cos2b}=tg(a+b)$

Answer 1

$cfrac{sin2a+sin2b}{cos2a+cos2b}= cfrac{2sin frac{2a+2b}{2}cosfrac{2a-2b}{2} }{2cos frac{2a+2b}{2}cosfrac{2a-2b}{2}}= cfrac{sin frac{2a+2b}{2} }{cos frac{2a+2b}{2}}= cfrac{sin (a+b)}{cos (a+b)}=mathrm{tg}(a+b)$