It is known that $\operatorname{tg} A+\operatorname{tg} B=2$ and $\operatorname{ctg} A+\operatorname{ctg} B=3$. Find $\operatorname{tg}(A+B)$.
$\frac{2}{\operatorname{tg} A \operatorname{tg} B}=\frac{\operatorname{tg} A+\operatorname{tg} B}{\operatorname{tg} A \operatorname{tg} B}=\operatorname{ctg} A+\operatorname{ctg} B=3$, hence $\operatorname{tg} A \operatorname{tg} B=2 / 3$. Therefore,

$\operatorname{tg}(A+B)=\frac{\operatorname{tg} A+\operatorname{tg} B}{1-\operatorname{tg} A \operatorname{tg} B}=\frac{2}{1-\frac{2}{3}}=6$.

## Answer

6.