9.191. $2 \cos x(\cos x-\sqrt{8} \tan x)<5$.
Solution.

Domain of definition: $\cos x \neq 0$.

Rewrite the inequality as $2 \cos x\left(\cos x-\sqrt{8} \frac{\sin x}{\cos x}\right)-50, \\ \cos x \neq 0\end{array} \Leftrightarrow\right.\right.$

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-0694.jpg?height=285&width=641&top_left_y=596&top_left_x=172)

From this, $x \in\left(2 \pi n-\frac{\pi}{4}+2 \pi n ; \frac{\pi}{2}+2 \pi n\right) \cup\left(\frac{\pi}{2}+2 \pi n ; \frac{5 \pi}{4}+2 \pi n\right), n \in Z$.

Answer: $x \in\left(2 \pi n-\frac{\pi}{4}+2 \pi n ; \frac{\pi}{2}+2 \pi n\right) \cup\left(\frac{\pi}{2}+2 \pi n ; \frac{5 \pi}{4}+2 \pi n\right), n \in Z$.