7) (sinx + cosx)² = 2;

Решим уравнение $$(sinx + cosx)^2 = 2$$

$$sin^2x + 2sinxcosx + cos^2x = 2$$

$$1 + 2sinxcosx = 2$$

$$2sinxcosx = 1$$

$$sin2x = 1$$

$$2x = \frac{\pi}{2} + 2\pi n, n \in Z$$

$$x = \frac{\pi}{4} + \pi n, n \in Z$$

Ответ: $$x = \frac{\pi}{4} + \pi n, n \in Z$$