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Question

Let f(θ)=sinθ(sinθ+sin3θ).Thenf(θ)is

A
0onlywhenθ 0
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B
0forallralθ
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C
0forallrealθ
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D
0onlywhenθ 0
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Solution

The correct option is C 0forallrealθ
f(θ)=sinθ(sinθ+sin3θ)=(sinθ+3sinθ4sin3θ).sinθ=(4sinθ4sin3θ)sinθ=sin2θ(44sin2θ)=4sin2θ(1sin2θ)=4sin2θcos2θ=(2sinθcosθ)2=(sin2θ)20\\
which is true for all θ.

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