If 0 ≤ x < π 2 , then the number of values of x for which sin x - sin 2 x + sin 3 x = 0 , is:

Step-by-step solution

sin x - sin 2 x + sin 3 x = 0 ⇒ sin x + sin 3 x - sin 2 x = 0 ⇒ 2 sin 2   x   . cos x - sin 2 x = 0 ⇒ sin 2 x = 0 or cos x = 1 2 ⇒ 2 x = 0 or x = π 3 ⇒ x = 0 or   x = π 3 ∴ Number of solutions = 2