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Question:

If 0 ≤ x < π/2, the number of values of x for which sinx - sin2x + sin3x = 0, is

2

3

4

1

Solution:

sinx - sin2x + sin3x = 0 ⇒ (sinx + sin3x) - sin2x = 0 ⇒ 2sin2x cosx - sin2x = 0 ⇒ sin2x(2cosx - 1) = 0 ⇒ sin2x = 0 or cosx = 1/2 ⇒ x = 0, π/3