# MATH ANALYSIS

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I need help solving this problem algebraically, but I need to learn step by step!!
Thanks so much

cos 2x=cos x

How do I do it?

• MATH ANALYSIS -

you should know that
cos 2x = 2cos^2 x - 1

so we have
2cos^2 x - 1 = cosx
2cos^2 x - cosx - 1 = 0
(2cosx + 1)(cosx -1) = 0
cosx = -1/2 or cosx = 1

x = 120° or 240° or x = 0 or 360
x = 0, 2π/3, 4π/3, 2π

• MATH ANALYSIS -

Thanks!

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