2. Each of the four numbers $-\sqrt{2} ; -1 ; -\frac{1}{2} ; 0$ is the result of one of the four arithmetic operations $\cos x + \cos y$, $\cos x - \cos y$, $\cos x \cdot \cos y$, $\cos x : \cos y$ on the numbers $\cos x, \cos y$ for some $x$ and $y$. Find all permissible pairs $(x ; y)$ for this.
Answer: $x= \pm \frac{3 \pi}{4}+2 \pi k, k \in Z, y= \pm \frac{\pi}{4}+2 \pi n, n \in Z$.