2.2. cos(1/2 x - π/4) = -√2/2;

Решим уравнение:

$$cos(\frac{1}{2}x - \frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$$

\(\frac{1}{2}x - \frac{\pi}{4} = arccos(-\frac{\sqrt{2}}{2})\)

\(\frac{1}{2}x - \frac{\pi}{4} = \frac{3\pi}{4} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \frac{3\pi}{4} + \frac{\pi}{4} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = \pi + 2\pi k, k \in Z\)

$$x = 2\pi + 4\pi k, k \in Z$$

или

\(\frac{1}{2}x - \frac{\pi}{4} = -\frac{3\pi}{4} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = -\frac{3\pi}{4} + \frac{\pi}{4} + 2\pi k, k \in Z\)

\(\frac{1}{2}x = -\frac{\pi}{2} + 2\pi k, k \in Z\)

$$x = -\pi + 4\pi k, k \in Z$$

Ответ: $$x = 2\pi + 4\pi k, k \in Z$$ или $$x = -\pi + 4\pi k, k \in Z$$