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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 = \frac{1}{3} - \frac{\tan 3x}{\tan x}

and

q = 1 - 3 \tan^2 x, \quad 0 < x < \pi, \quad x \neq \frac{\pi}{2}

[NDA II 2023]

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Question : 75 of 120

Marks: +1, -0

What is pq equal to ?

1
2
$\;\frac{8}{3}$
$-\;\frac{8}{3}$

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