## Task B-3.1.

Solve the inequality

$$
8 \sin x \cos x \cos 2 x>1
$$
## Solution.

$$
\begin{array}{r}
4 \cdot 2 \cdot \sin x \cos x \cdot \cos 2 x>1 \Leftrightarrow \\
4 \cdot \sin 2 x \cdot \cos 2 x>1 \Leftrightarrow \\
2 \sin 4 x>1 \Leftrightarrow \sin 4 x>\frac{1}{2}
\end{array}
$$

The last inequality holds if $4 x \in\left\langle\frac{\pi}{6}+2 k \pi, \frac{5 \pi}{6}+2 k \pi\right\rangle, k \in \mathbb{Z}$, 2 points respectively, $x \in\left\langle\frac{\pi}{24}+\frac{k \pi}{2}, \frac{5 \pi}{24}+\frac{k \pi}{2}\right\rangle, k \in \mathbb{Z}$.