Question

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

Answer 1

$cos 2x - cos 6x = 0$

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

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

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

$2sin 4x sin 2x = 0$

$sin 4x sin 2x = 0$

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

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

Ответ: $x = dfrac{pi n}{4}, n in Z$