2 cosx sinx Squareroot 3 cosx 0 Find all angles in radians

2 cos(x) sin(x) - Squareroot 3 cos(x) = 0 Find all angles in radians that satisfy the equation. For each solution enter first the angle solution in [0, 2pi] then the period. When 2 or more solutions are available enter them in increasing order of the angles. (e.g. x = pi/2 + 2kpi or x = 3 pi/2 + 2k pi etc.)

Solution

Given

2*sin x * cos x - 3*cos x = 0

cos x*(2*sin x - 3) = 0

cos x = 0 ========> x = pi/2 + n*pi

and (2*sin x - 3) = 0 =========> sin x = 3/2 ====> x = pi/3