Find the exact solutions of the equation in the interval [0, 2π).

Question

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

Answer 1

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

if cosx = -1/2, then
x = 120° or 240°
x = 2π/3 or x = 4π/3

if cosx = 1
x = 0 or x = 2π

x = 0, 2π/3 , 4π/3 , 2π

Answer 2

How did you factor the 2 cos^2x - 1 - cosx?

Answer 3

2cos^2 x - cosx - 1
compare to
2a^2 - a - 1
= (2a +1)(a - 1) , where a = cosx

Answer 4

Ah, okay. Thank you!