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UPSC NDA I 2015 Mathematics Solved Paper

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For the next two(2) items that follow:

Let

\alpha

be the root of the equation

25 \cos^{2} \theta + 5 \cos \theta - 12 = c

, where

\; \frac{\pi}{2} < \alpha < \pi

.

[NDA I 2015]

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Question : 34 of 120

Marks: +1, -0

What is sin2α equal to?

$\frac{24}{25}$
$-\frac{24}{25}$
$-\frac{5}{12}$
$-\frac{21}{25}$

Solution:

Therefore, from the above solution, we have obtained

\cos\alpha = \frac{-3}{5}

\sin\alpha = \frac{4}{5}

\tan\alpha = \frac{-4}{3}

\therefore \sin 2\alpha = 2 \sin \alpha \cos \alpha

= 2 \left( \frac{4}{5} \right) \left( \frac{-3}{5} \right)

= \frac{-24}{25}

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