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Решите задачу:

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

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