How do you find the point of intersection of cosx=cos2x?

Answer 1

cosx = 2cos^2 x - 1
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 x = 360°

Those are not "points of intersection" , they are solutions to your equation.
You can't find points of intersection, since you don't have y variable in your equation.