3.160. $\frac{5}{6+7 \sin 2 \alpha}$, if $\operatorname{tg} \alpha=0.2$.
## Solution.

$$
\begin{aligned}
& \frac{5}{6+7 \sin 2 \alpha}=\frac{5}{6+\frac{14 \tan \alpha}{1+\tan^{2} \alpha}}=\frac{5+5 \tan^{2} \alpha}{6+6 \tan^{2} \alpha+14 \tan \alpha}= \\
& =\frac{5+5 \cdot 0.04}{6+6 \cdot 0.04+14 \cdot 0.2}=\frac{65}{113}
\end{aligned}
$$

Answer: $\frac{65}{113}$.