Question

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

Answer 1

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