cos 2x = sin (2x - 30°)

Question

Solve the following questions for x is in between 0° to 360°

Answer 1

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