cos(2x) = sin(2x - 30)
sin(Pi/2 - 2x) = sin(2x - 30) {sin(A) = cos(Pi/2 - A)}
Pi/2 - 2x = 2x - Pi/6 {30 º = Pi/6 }
Pi/2 + Pi/6 = 4x
4x = 2Pi/3
x = Pi/6 = 30
The equation cos(2x) = sin(2x - 30) is also satified with 2x = 60 + n*Pi, n = 0, +/-1, +/- 2, ...
i.e. 2x = 60, 2x = 60 + 180, 2x = 60 + 360, 2x = 60 + 540
or, 2x = 60, 2x = 240, 2x = 420, 2x = 600
i.e. x = 30, 120, 210, 300