1. The range of the inclination angle of the line $x \cdot \cos \alpha+y+1=0$ is
1. $\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}, \pi\right)$. From $y=-\cos \alpha \cdot x-1$ and $|-\cos \alpha| \leqslant 1$ we know $|\tan \theta| \leqslant 1$, thus $\theta \in\left[0, \frac{\pi}{4}\right] \cup\left[\frac{3 \pi}{4}\right.$, $\pi)$.