[JEE Advanced 2000] let f theta sin theta sin theta sin 3 theta then f theta is
Let $f(\theta)=\sin\theta(\sin\theta+\sin3\theta)$. Then $f(\theta)$ is
(a) $\ge0$ only when $\theta\ge0$
(b) $\le0$ for all real $\theta$
(c) $\ge0$ for all real $\theta$
(d) $\le0$ only when $\theta\le0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (c) $\ge0$ for all real $\theta$
$\sin\theta+\sin3\theta=2\sin2\theta\cos\theta$, so $f=\sin\theta\cdot2\sin2\theta\cos\theta=4\sin^2\theta\cos^2\theta=\sin^22\theta\ge0$ for all $\theta$.
JEE Advanced 2000 · Trigonometry — verified solution by the Vidaara Team.
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