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UPSC NDA I 2015 Mathematics Paper

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Question Numbers: 33-34

Direction: Let

\alpha

be the root of the equation

25 \cos^{2} \theta + 5 \cos \theta - 12 = 0

, where

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

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Question : 34 of 120

Marks: +1, -0

What is sin 2α equal to?

$24/25$
$-24/25$
$-5/12$
$-21/25$

Solution:

Concept:

Use the double-angle formula:

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

.

Explanation:

From the given problem,

\sin \alpha = \frac{3}{5}

and

\cos \alpha = -\frac{4}{5}

.

Substitute into the formula:

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

.

Multiply the numerators and denominators:

\sin 2\alpha = 2 \times \frac{-12}{25} = \frac{-24}{25}

.

Answer:

\displaystyle -\frac{24}{25}

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