Question

Тригонометрическое уравнение

Answer 1

Cos 2x = 1 - cos (3p/2 + x) 
cos (3p/2 + x)  = sin x.
cos 2x - 1 = sin x
cos^2 x - sin^2 x - sin^2 x - cos^2x - sin x = 0
-2sin^2x -sin x = 0
-sin x ( 2sin x + 1) = 0
- sin x =0
sin x = 0
x= pm, m ∈ Z.

2 sin x = -1
sin x = -1/2
x= -p/6 + 2pk, k ∈ Z.
x= -5p/6 + 2pn, n ∈ Z.