2 sin x cos x + cos x = 0

cos x [ 2 sin x + 1 ] = 0

cos x = 0 , sin x = - 1/2

x = π/2 . 3π/2 , 7π/6 , 11π/6

sin 2x = 2 sin x cos x so you have 2 sin x cos x + cos x = 0

Factor: cos x (2 sin x + 1) = 0

so either cos x = 0 or 2 sin x = -1 → sin x = -1/2 and go from there.