Question

Cos 2x – cos 6x = 0
Помогите пожалуйста!

Answer 1

$\cos 2x - \cos 6x = 0$

$\cos a - \cos b = -2\sin \dfrac{a+b}{2} \sin \dfrac{a - b}{2}$

$-2\sin \dfrac{2x+6x}{2} \sin \dfrac{2x - 6x}{2} = 0$

$-2\sin 4x \sin -2x = 0$

$2\sin 4x \sin 2x = 0$

$\sin 4x \sin 2x = 0$

$1) \ \sin 4x = 0; \ 4x = \pi n, \ n \in Z; \ x = \dfrac{\pi n}{4}, \ n \in Z$

$2) \ \sin 2x = 0; \ 2x = \pi k, \ k \in Z; \ x = \dfrac{\pi k}{2}, \ k \in Z$

Ответ: $x = \dfrac{\pi n}{4}, \ n \in Z$