4- 120 If $\operatorname{tg} x+\operatorname{tg} y=25$, and $\operatorname{ctg} x+\operatorname{ctg} y=30$. Find $\operatorname{tg}(x+y)$.
[Solution] From $\operatorname{ctg} x+\operatorname{ctg} y=30$ we get

then
$$
\frac{1}{\operatorname{tg} x}+\frac{1}{\operatorname{tg} y}=30 \text {, }
$$

then $\frac{\operatorname{tg} x+\operatorname{tg} y}{\operatorname{tg} x \cdot \operatorname{tg} y}=30$,
which means $\frac{25}{\operatorname{tg} x \cdot \operatorname{tg} y}=30$,
$$
\operatorname{tg} x \cdot \operatorname{tg} y=\frac{5}{6} .
$$

Therefore, $\operatorname{tg}(x+y)=\frac{\operatorname{tg} x+\operatorname{tg} y}{1-\operatorname{tg} x \cdot \operatorname{tg} y}=\frac{25}{1-\frac{5}{6}}=150$.