Question

2sin^2theta - 2 cos theta =1/2 , find theta

Answer 1

Let theta be x

We are given, 2sin^2 x - 2cos x = 1/2

                 so, sin^2 x - cos x = 1/4

                      so, 1 - cos^2 x - cos x = 1/4

                     = cos^2 x + cos x = 1 - 1/4

                     = cos^2 x + cos x = 3/4

                    = 4cos^2 x + cos x = 3

                    = 4cos^2 x + cosx - 3 = 0

               Solving above equation,

          4cos x = 3 or cos x = - 1

    hence , cos x = 3/4 or cos x = -1

Hence, x or theta = 0.722° or 180°