Решить уравнение   Cos2x=2Cosx-1

[latex] cos2x = 2cosx - 1\ 2{cos ^2}x - 1 - 2cos x + 1 = 0\ 2{cos ^2}x - 2cos x = 0\ 2cos xleft( {cos x - 1} ight) = 0\ left[ egin{array}{l} 2cos x = 0\ cos x = 1 end{array} ight.left[ egin{array}{l} x = frac{pi }{2} + pi n,n in z\ x = 2pi k,k in z end{array} ight. [/latex]