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Let $\alpha$ be the root of the equation $25 \cos ^{2} \theta+5 \cos \theta-12=0$,
where $\frac{\pi}{2} < \alpha < \pi$
What is $\sin 2 \alpha$ equal to?
Options:
where $\frac{\pi}{2} < \alpha < \pi$
What is $\sin 2 \alpha$ equal to?
Solution:
2502 Upvotes
Verified Answer
The correct answer is:
$\frac{-24}{25}$
$\sin 2 \alpha=2 \sin \alpha \cdot \cos \alpha$
$=2\left(\frac{3}{5}\right)\left(\frac{-4}{5}\right)$
$=\frac{6}{5} \times \frac{-4}{5}=\frac{-24}{25}$
$\therefore \quad$ Option (b) is correct.
$=2\left(\frac{3}{5}\right)\left(\frac{-4}{5}\right)$
$=\frac{6}{5} \times \frac{-4}{5}=\frac{-24}{25}$
$\therefore \quad$ Option (b) is correct.
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