Question

решить cos(x) + sin(3x)=0​

Answer 1

$cosx + sin(3x) = 0\\sin(\frac{\pi}{2} -x)+sin(3x)=0\\ 2sin(\frac{\frac{\pi}{2} -x + 3x}{2})cos(\frac{\frac{\pi}{2} -x - 3x}{2})=0\\sin(\frac{\pi}{4}+\frac{x}{2})cos(\frac{\pi}{4}-x)= 0\\sin(\frac{\pi}{4}+\frac{x}{2}) = 0 = \frac{\pi}{4}+\frac{x}{2} = \pi n, n \in Z = x = -\frac{\pi}{2} + 2\pi n, n \in Z\\cos(\frac{\pi}{4}-x) = 0 = \frac{\pi}{4}-x = \frac{\pi}{2} + \pi k, k \in Z = x = -\frac{\pi}{4} +2\pi k , k \in Z$