9.146. $\sin 4 x+\cos 4 x \operatorname{ctg} 2 x>1$.

9.146. $\sin 4x + \cos 4x \cot 2x > 1$.
## Solution.

Let's rewrite the inequality as

$$
\begin{aligned}
& \sin 4 x+\frac{\cos 4 x \cos 2 x}{\sin 2 x}>1 \Leftrightarrow \frac{\sin 4 x \sin 2 x+\cos 4 x \cos 2 x}{\sin 2 x}>1 \Leftrightarrow \\
& \Leftrightarrow \frac{\cos 2 x}{\sin 2 x}>1, \operatorname{ctg} 2 x>1, \pi n<2 x<\frac{\pi}{4}+\pi n, \frac{\pi n}{2}<x<\frac{\pi}{8}+\frac{\pi n}{2}, n \in Z \\
& \frac{\pi n}{2}<x<\frac{\pi}{8}(4 n+1), n \in Z \\
& \text { Answer: } x \in\left(\frac{\pi n}{2} ; \frac{\pi}{8}(4 n+1)\right), n \in Z
\end{aligned}
$$