Question

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

Answer 1

Answer:

Please see the attachment

Answer 2

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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