Solve Trig Identity Problem: Find all values for cos2x=cosx

[yeyspaz]

I have this trig identity problem i need to solve

cos2x=cosx

I have to find all the values of x, and i know the answer is x=0°+120°, but i can figure ou how. I've tried it over and over and my answer turns out to x=0°=180°. Please help, thank you.

 

[Tide]

First, 180 is NOT equal to 0. Second, 180 degrees is obviously not a solution (substitiute back into the equation to see this).

HINT: $$\cos 2x = \cos^2 x - \sin^2 x$$