Task B-3.5. Solve the inequality $x \cos x-1<x-\cos x$.
## Solution.

The inequality can be written in the form $(x+1)(\cos x-1)<0$ and $\cos x \neq 1$.

It follows that $x>-1, x \neq 2 k \pi, k \in \mathbb{Z}$.

Therefore, the solution to the inequality is $x \in (-1,+\infty) \backslash \{2 k \pi: k \in \mathbb{Z}\}$.