Question

cos^2(x)+cos(x)=cos(2x)

Answer 1

find x ?

Answer 2

It's asking to find all solutions in interval \[[0,2\pi)\]

Answer 3

cos^2x - cos x = 0
cos x ( cos 2x - 1) = 0
cos x = 0 or cos 2x -1 = 0
cos 2x =1
cos x =0 , cos 2x = 1
see if i did wrong in my steps ...

Answer 4

x = cos-1 ( 0) 2x = cos-1 (1)
x = Pi/2

Answer 5

2nd value : x = 2Pi - Pi/2 = 3/2 Pi

Answer 6

cos2x=2cos^2x-1 would be the first step I would use. Then move everything to one side and get:

cos^2x-cosx-1=0 From there, it doesn't factor so you will have to use a quadratic fromula.