Verified answer

18 sin x cos x - 9 cos x = 0

9 cos x [ 2 sin x - 1 ] = 0

cos x = 0 , sin x = 1/2

x = π/2 , 3π/2 , π/6 , 5π/6

Divide both sides by 9 and replace sin 2x with 2 sin x cos x

2 sin x cos x = cos x

2 sin x cos x - cos x = 0

cos x( 2 sin x - 1) = 0

so either cos x = 0 or sin x = 1/2

x = π/2, 3π/2, π/6 or 5π/6