$4.35 \operatorname{tg} 435^{\circ}+\operatorname{tg} 375^{\circ}$.

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$4.35 \tan 435^{\circ}+\tan 375^{\circ}$.
### 4.35 We have

$$
\begin{aligned}
& \tan 435^{\circ} + \tan 375^{\circ} = \tan 75^{\circ} + \tan 15^{\circ} = \frac{\sin 90^{\circ}}{\cos 75^{\circ} \cos 15^{\circ}} = \\
& = \frac{2}{\cos 90^{\circ} + \cos 60^{\circ}} = 4
\end{aligned}
$$

Here, reduction formulas, as well as (4.23) and (4.26), were used.