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Question

Let f(θ)=sinθ(sinθ+sin3θ),thenf(θ)


A

≥ 0 only when θ≥ 0

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B

≤ 0 for all real θ

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C

≥ 0 for all real θ

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D

≤ 0 only when θ ≤0

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Solution

The correct option is C

≥ 0 for all real θ


Here ,f(θ)=sinθ(sinθ+sin3θ)

=sinθ(sinθ+sin3θ4sin3θ)=4sin2θ(1sin2θ)

4sin2θ cos2θ=(sin2θ)2
f(θ) 0 for all real θ.


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