Find all solutions in the interval [0,2π) of the equation.

2sin (x) cos (x) - sin (x) + 2cos (x) - 1 = 0.

Step-by-step explanation:

2sin (x) cos (x) - sin (x) + 2cos (x) - 1 = 0

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

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

sinx=-1 or cosx = 1/2

+) sinx=1 = > x = pi/2 + k*2pi

+) cosx=1/2 = > x = pi/3 + k*2pi or x=-pi/3 + k*2pi

x€ [0,2pi] = > x = pi/2, pi/3.