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

which means

so
$$\begin{array}{l}
\frac{\operatorname{tg} x+\operatorname{tg} y}{\operatorname{tg} x \cdot \operatorname{tg} y}=30 \\
\frac{25}{\operatorname{tg} x \cdot \operatorname{tg} y}=30 \\
\operatorname{tg} x \cdot \operatorname{tg} y=\frac{5}{6}
\end{array}$$