Question

докажите тождество tga-tgb=sin(a-b)/cosacosb

Answer 1

$tg \alpha -tg \beta = \frac{Sin \alpha }{Cos \alpha }- \frac{Sin \beta }{Cos \beta }= \frac{Sin \alpha Cos \beta -Cos \alpha Sin \beta }{Cos \alpha Cos \beta }= \frac{Sin( \alpha - \beta) }{Cos \alpha Cos \beta }$