$9.296 \frac{\cos x+2 \cos ^{2} x+\cos 3 x}{\cos x+2 \cos ^{2} x-1}>1$.

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$9.296 \frac{\cos x+2 \cos ^{2} x+\cos 3 x}{\cos x+2 \cos ^{2} x-1}>1$.
Solution. $\frac{(\cos x+\cos 3 x)+2 \cos ^{2} x}{\cos x+\cos 2 x}>1 \Leftrightarrow \frac{\cos x \cdot(\cos 2 x+\cos x)}{\cos 2 x+\cos x}>\frac{1}{2} \Leftrightarrow$ $\Leftrightarrow\left\{\begin{array}{l}\cos x>\frac{1}{2}, \\ 2 \cos ^{2} x+\cos x-1 \neq 0\end{array} \Leftrightarrow \cos x>\frac{1}{2} \Leftrightarrow-\frac{\pi}{3}+2 \pi n<x<\frac{\pi}{3}+2 \pi n\right.$.

Answer: $x \in\left(\frac{\pi}{3}(6 n-1) ; \frac{\pi}{3}(6 n+1)\right)$.

## $9.2978 \sin ^{4} x-8 \sin ^{2} x+\sin x-1<0$.

Solution. $8 \sin ^{2} x \cdot\left(\sin ^{2} x-1\right)+(\sin x-1)<0$.

Both terms on the left side are non-positive. Therefore, the inequality is equivalent to the following condition:

$\sin x \neq 1$ or $x \neq \frac{\pi}{2}+2 \pi n$.

Answer: $\quad x \neq \frac{\pi}{2}(4 n+1)$.