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Question

Let f(θ)=sin θ(sin θ+sin 3θ). Then f(θ)

A
only when θ0
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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 θ0
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Solution

The correct option is C 0, for all real θ
It is given,
f(θ)=sinθ(sinθ+sin3θ)=(sinθ+3sinθ4sin3θ)sinθ=(4sinθ4sin3θ)sinθ=sin2θ(44sin2θ)=4sin2θcos2θ=(2sinθcosθ)2=(sin2θ)20
Which is true for all θ

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