Let f (θ) = sin θ (sin θ + sin 3 θ). Then f (θ) :
(A) ≥ 0 only when θ ≥ 0 (B) ≤ 0 for all real θ
(C) ≥ 0 for all real θ (D) ≤ 0 only when θ ≤ 0

f(x)= sinx(sinx+sin3x)

     =sinx.2sin2x.cosx

     =sin²2x

f(x)≥0 for all real x and lies in region[ 0 , 1]

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IIT Kgp - 05 batch