2cos(x)-1=0

2 cos = 1

cos (x ) = 1/2

ARCOS(X) = x = arcos(1/2) = 60 degrees or 300 degrees ( pi/3 radians or 5pi/6 radians)

What about cos2x-1=0? I'm only getting pi as a solution.

Coc(2x) = 1 x = pi or 0 (and 2pi)