4.39 Given: $\operatorname{ctg} \alpha=\frac{3}{4}, \operatorname{ctg} \beta=\frac{1}{7}, 0<\alpha<\frac{\pi}{2}, 0<\beta<\frac{\pi}{2}$. Find $\alpha+\beta$.
4.39 Note that $\operatorname{tg} \alpha=\frac{4}{3}, \operatorname{tg} \beta=7$. Then, by formula (4.11), we find

$$
\operatorname{tg}(\alpha+\beta)=\frac{\frac{4}{3}+7}{1-\frac{28}{3}}=-1
$$

Since by the condition $0<\alpha+\beta<\pi$, then $\alpha+\beta=\frac{3 \pi}{4}$.