Question

Упростите выражение

Answer 1

$displaystylemathtt{frac{tga+tgb}{ctga+ctgb}=frac{frac{sina}{cosa}+frac{sinb}{cosb}}{frac{cosa}{sina}+frac{cosb}{sinb}}=frac{frac{sinacosb}{cosacosb}+frac{cosasinb}{cosacosb}}{frac{cosasinb}{sinasinb}+frac{sinacosb}{sinasinb}}=frac{frac{sinacosb+cosasinb}{cosacosb}}{frac{cosasinb+sinacosb}{sinasinb}}}$

$displaystylemathtt{frac{sinacosb+cosasinb}{cosacosb}:frac{cosasinb+sinacosb}{sinasinb}=}\\displaystylemathtt{frac{sinacosb+cosasinb}{cosacosb}*frac{sinasinb}{cosasinb+sinacosb}=}\\displaystylemathtt{frac{sinasinb}{cosacosb}=tgatgb}$