Jika 2 sin x + 3 cot x - 3 csc x =0 dengan 0

2Sin x + 3 Cot x - 3Csc x = 0
2Sin x + 3(Cos x / Sin x) - (3/Sin x) = 0
(2Sin²x + 3Cosx - 3)/Sinx = 0
2Sin²x + 3Cosx - 3 = 0

Berdasarkan Teorema Vietta
Sin x . Cos x = c/a
Sin x . Cos x = -3/2

2 sin x + 3 cot x - 3 cosec x = 0
2 sin x + 3(cos x)/(sin x) - 3(1)/(sin x) = 0 ====> kali sin x
2 sin^2 x + 3 cos x - 3 = 0
2 (1 - cos^2 x) + 3 cos x - 3 = 0
2 - 2 cos^2 x + 3 cos x - 3 = 0
-2 cos^2 x + 3 cos x - 1 = 0
2cos^2 x - 3 cos x + 1 = 0
Misal cos x = a
2a^2 - 3a + 1 = 0
(2a - 1)(a - 1) = 0
a = 1/2 atau a = 1
Cos x = 1/2 atau cos x = 1
Karena 0 < x < π/2 maka
Cos x = 1/2 => cos x = cos 60° => x = 60°

Sin x . cos x = sin 60° . cos 60° = 1/2 √3 . 1/2 = 1/4 √3