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NDA Math Definite Integrals

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For the next two(2) items that follow:

Consider the integrals

A=\int\limits_{0}^{\pi} \; \frac{\sin x \, dx}{\sin x + \cos x}

and

B=\int\limits_{0}^{\pi} \; \frac{\sin x \, dx}{\sin x - \cos x}

[NDA II 2015]

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Question : 46 of 62

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Which one of the following is correct ?

$A = 2B$
$B = 2A$
$A = B$
$A = 3B$

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