9. The solution to the inequality $\sqrt{3} \sin x-\cos x+1<0$ is
9. $\left(2 k \pi-\frac{2 \pi}{3}, 2 k \pi\right), k \in \mathbf{Z}$.
$\sqrt{3} \sin x-\cos x+11$, i.e., $2 \cos \left(x+\frac{\pi}{3}\right)>1$, solving gives $2 k \pi-\frac{\pi}{3} < x+\frac{\pi}{3} < 2 k \pi+\frac{\pi}{3}$, so $x \in \left(2 k \pi-\frac{2 \pi}{3}, 2 k \pi\right), k \in \mathbf{Z}$.