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

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⩾

0

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θ ⩾ 0

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θ

⩾ 0

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θ

⩽ 0

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θ ⩽ 0

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detailed solution

Correct option is C

$f (θ)$ $= \sin θ$ $(\sin θ + \sin 3 θ)$

$= \sin θ . 2 \sin 2 θ \cos θ = 2 \sin θ \cos θ \sin 2 θ$

$= \sin^{2} 2 θ ⩾ 0$ for all $θ$

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Letf(θ)=sin⁡θ(sin⁡θ+sin⁡3θ).Thenf(θ)