Question

Доказать тождество: sin(α+β)/sin(α-β)=tgα+tgβ/tgα-tgβ

Answer 1

(sina/cosa+sinb/cosb)/(sina/cosa-sinb/cosb)=(sin(a+b)/cosacosb)/(sin(a-b)/cosacosb)=sin(a+b)/sin(a-b)

Answer 2

$frac{sin(alpha+beta)}{sin(alpha-beta)} \ frac{sinalpha cosbeta+cosalpha sinbeta}{sinalpha cosbeta-cosalpha sinbeta} \ frac{tgalpha + tgbeta}{tgalpha - tgbeta}$