The number of solutions of the equation sin 9 x + sin 3 x = 0 in the closed interval 0 , 2 π is

Step-by-step solution

Given trigonometric equation is sin 9 x + sin 3 x = 0 ⇒   2 sin 6 x cos 3 x = 0 ∴ either sin 6 x = 0 or cos 3 x = 0 for x ∈ 0 , 2 π sin 6 x = 0 ⇒   x = 0 ,   π 6 ,   π 3 ,   π 2 ,   2 π 3 ,   5 π 6 ,   π ,   7 π 6 ,   4 π 3 ,   3 π 2 ,   5 π 3 ,   2 π and 3 x = 0 ⇒   x = π 6 ,   π 2 ,   5 π 6 ,   7 π 6 ,   3 π 2 ,