If 0 ≤ x < π/2,
then the number of values of x for which sin x – sin 2x + sin 3x = 0, is
(A) 2 (B) 1
(C) 3 (D) 4
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answer : option (A) 2
given, sinx - sin2x + sin3x = 0
using formula, sinC + sinD = 2sin(C + D)/2. cos(C - D)/2
so, sinx - sin2x + sin3x = 0
⇒2sin(x + 3x)/2. cos(3x - x)/2 - sin2x = 0
⇒2sin2x. cosx - sin2x = 0
⇒sin2x [2cosx - 1] = 0
sin2x = 0 or, cosx = 1/2
from sin2x = 0, x = 0 for 0 ≤ x < π/2
from cosx = 1/2 , x = π/3 for 0 ≤ x < π/2
hence x = 0, π/3
there are two values of given equation.
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