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UPSC NDA II 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :

Let

p=\cos\left(\frac{\pi}{5}\right)\cos\left(\frac{2\pi}{5}\right)

and

q=\cos\left(\frac{4\pi}{5}\right)\cos\left(\frac{8\pi}{5}\right)

.

[NDA II 2023]

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Question : 74 of 120

Marks: +1, -0

What is the value of pq?

$-\frac{1}{16}$
$-\frac{1}{4}$
$\frac{1}{4}$
$\frac{1}{16}$

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