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

Question

Thanks so much

cos 2x=cos x

How do I do it?

Answer 1

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
in radians
x = 0, 2π/3, 4π/3, 2π

Answer 2

Thanks!