Question

Помогите решить уравнение sin10x+cos10x=-√2sin8x

Answer 1

$4) \sin(10x) + \cos(10x) = - \sqrt{2} \sin(8x) \\ \sin {}^{2} (10x) + \cos {}^{2} (10x) = 2 \sin {}^{2} (8x) \\ 2 \sin{}^{2} (8x) = 1 \\ \sin {}^{2} (8x) = \frac{1}{2} \\ \frac{1 - \cos(16x) }{2} = \frac{1}{2} \\ 1 - \cos(16x) = 1 \\ \cos(16x) = 0 \\ 16x = \frac{\pi}{2} + 2\pi n \: \: \: \: n \in \: z \\ x = \frac{\pi}{32} + \frac{1}{8} \pi n \: \: \: \: n \in \: z$