Question

sin 5x + sin x = 0
Помогите ​

Answer 1

$\sin 5x+\sin x=0\Leftrightarrow \sin x=-\sin 5x\Rightarrow x=\left \{ \pi+5x+2\pi k,-5x+2\pi k \right \},k \in \mathbb{Z}$

$x=\pi +5x+2\pi k\Leftrightarrow -4x=\pi +2\pi k\Rightarrow x=-\frac{\pi}{4}+\frac{\pi k}{2},k \in \mathbb{Z}$

$x=-5x+2\pi k\Leftrightarrow 6x=2\pi k\Rightarrow x=\frac{\pi k}{3},k \in \mathbb{Z}$