Question

Доказать тождество: cos (a-b) / cos a sin b=tga+ctgb 

Answer 1

$\dfrac{cos(a-b)}{cosasinb} = \dfrac{cosacosb+sinasinb}{cosasinb} = \dfrac{cosacosb}{cosasinb} + \dfrac{sinasinb}{cosasinb} =\\ = \dfrac{cosb}{sinb} + \dfrac{sina}{sinb} =ctgb+tga$
Доказано.