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Q.

$The greatest (or) least value of 2 \sin^{2} θ + 4 {cosec}^{2} θ is$

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a

$2 \sqrt{2}$

b

$4 \sqrt{2}$

c

2

d

4

answer is B.

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Detailed Solution

$A . M \geq G . M$

$\Rightarrow \frac{2 \sin^{2} θ + 4 {cosec}^{2} θ}{2} \geq \sqrt{(2 \sin^{2} θ) (4 {cosec}^{2} θ)}$

$2 \sin^{2} θ + 4 {cosec}^{2} θ \geq 4 \sqrt{2}$

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