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

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To solve the equation cos(2x) = cos(x), start by using the identity cos(2x) = cos²(x) - sin²(x). This leads to the equation cos²(x) - sin²(x) - cos(x) = 0. By substituting sin²(x) with 1 - cos²(x), the equation can be rewritten in terms of cos(x) only. Solving this quadratic equation yields the solutions x = 0° and x = 120°. The correct values for x are thus confirmed as 0° + 120°.
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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.:rolleyes:
 
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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
 

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