Решите sin(x) + cos(x) = √2/2 sin(x)

Решение: $$sin(x) + cos(x) = \frac{\sqrt{2}}{2} sin(x)$$ $$cos(x) = \frac{\sqrt{2}}{2} sin(x) - sin(x)$$ $$cos(x) = sin(x)(\frac{\sqrt{2}}{2} - 1)$$ $$cos(x) = sin(x)(\frac{\sqrt{2} - 2}{2})$$ $$\frac{cos(x)}{sin(x)} = \frac{\sqrt{2} - 2}{2}$$ $$ctg(x) = \frac{\sqrt{2} - 2}{2}$$ $$x = arcctg(\frac{\sqrt{2} - 2}{2}) + \pi n, n \in Z$$ Ответ: x = $$arcctg(\frac{\sqrt{2}-2}{2})$$ + $$\pi n$$, n∈Z