7. Найдите нули функции f (x) = 2sin(\frac{\pi}{4}-x)-\sqrt{3}.

Найдем нули функции $$f(x) = 2sin(\frac{\pi}{4} - x) - \sqrt{3}$$.

$$2sin(\frac{\pi}{4} - x) - \sqrt{3} = 0$$

$$2sin(\frac{\pi}{4} - x) = \sqrt{3}$$

$$sin(\frac{\pi}{4} - x) = \frac{\sqrt{3}}{2}$$

$$\frac{\pi}{4} - x = (-1)^n arcsin(\frac{\sqrt{3}}{2}) + \pi n, n \in Z$$

$$\frac{\pi}{4} - x = (-1)^n \frac{\pi}{3} + \pi n, n \in Z$$

$$x = \frac{\pi}{4} - (-1)^n \frac{\pi}{3} - \pi n, n \in Z$$

Ответ: $$x = \frac{\pi}{4} - (-1)^n \frac{\pi}{3} - \pi n, n \in Z$$