Определить корни уравнения: 2 sin(x) + cos(x) - √2 sin(x) = 0

Решение: $$2 sin(x) + cos(x) - \sqrt{2} sin(x) = 0$$ $$2 sin(x) - \sqrt{2} sin(x) = - cos(x)$$ $$sin(x) (2 - \sqrt{2}) = -cos(x)$$ $$\frac{sin(x)}{cos(x)} = \frac{-1}{2 - \sqrt{2}}$$ $$tg(x) = \frac{-1}{2 - \sqrt{2}}$$ $$tg(x) = \frac{-1}{2 - \sqrt{2}} * \frac{2 + \sqrt{2}}{2 + \sqrt{2}} = \frac{-(2 + \sqrt{2})}{4 - 2} = \frac{-(2 + \sqrt{2})}{2} = -1 - \frac{\sqrt{2}}{2}$$ $$x = arctg(-1 - \frac{\sqrt{2}}{2}) + \pi n, n \in Z$$ Ответ: $$x = arctg(-1 - \frac{\sqrt{2}}{2}) + \pi n, n \in Z$$