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Question

Let f(θ)=sinθ(sinθ+sin3θ). Then f(θ)

A
0 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
f(θ)=12[(1cos2θ)+(cos2θcos4θ)]

[1cos2θ=2sin2θand 2sinasinb=cos(ab)cos(a+b)]

=12(1cos4θ)=sin22θ0 real θ.

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