Question 970652
cos 2x=2 cos^2x-1

2cos^2 x-1-cos x=0

2 cos^2 x- cos x -1=0  Factor.

(2cos x +1) (cos x-1)=0

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

cos x=1 at 0 degrees   Cos 0 deg=cos 2*0 degrees

cos x=(-1/2) at pi/3 or 120 degrees.

cos x= (-1/2) at 2pi/3 or 240 degrees.

smallest value is 0
largest value is 2 pi/3