Find the solution

2cos2x-2cosx=0

x = 0, 2π/3, 4π/3

Step-by-step explanation:

2 cos (2x) - 2 cos x = 0

Use double angle formula.

2 (2 cos²x - 1) - 2 cos x = 0

Simplify.

4 cos²x - 2 - 2 cos x = 0

2 cos²x - 1 - cos x = 0

2 cos²x - cos x - 1 = 0

Factor.

(cos x - 1) (2 cos x + 1) = 0

Solve.

cos x = 1 or - ½

x = 0, 2π/3, 4π/3