3 sin 2x - 4 cos x + 3 sin x - 2=0

Question

3 sin 2x - 4 cos x + 3 sin x - 2=0

Answer 1

(3 sinx-2) (2 cosx+1) = 0

3 (sinx+sin2 x) = 4 cosx+2

3 sinx-4 cosx+6 sinx cosx-2 = 0

  x = 2 (pi n+tan^(-1)(1/2 (3-√5)))), n = Z

 

x = 2 (pi n+tan^(-1)(1/2 (3+√5)))), n = Z

x = 2/3 (3 pi n-pi), n = Z

 x = 2/3 (3 pi n+pi), n = Z