SATHEE: Functions 1 Question 8

Functions 1 Question 8

8.

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

(2000, 1M)

(a) $\geq 0$ , only when $θ \geq 0$

(b) $\leq 0$ , for all real $θ$

(d) $\leq 0$ , only when $θ \leq 0$

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Answer:

Correct Answer: 8. (c)

Solution:

It is given,

$\begin{aligned} f (θ) & = \sin θ (\sin θ + \sin 3 θ) \\ = (\sin θ + 3 \sin θ - 4 \sin^{3} θ) \sin θ \\ = (4 \sin θ - 4 \sin^{3} θ) \sin θ = \sin^{2} θ (4 - 4 \sin^{2} θ) \\ = 4 \sin^{2} θ \cos^{2} θ = (2 \sin θ \cos θ)^{2} \\ = (\sin 2 θ)^{2} \geq 0 \end{aligned}$

which is true for all $θ$ .

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Functions 1 Question 8

8.

Answer:

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