Question

lf $\alpha$ is a root of
25 $co{s}^2\theta +5cos\theta -12=0,\frac{\pi }{2}<\alpha <\pi$
then $sin2\alpha$ is equal to

• A. $24/25$
• B. $-24/25$
• C. $13/18$
• D. $-13/18$

Answer 1

The correct option is B $-24/25$

$25{\cos }^2\theta +5\cos \theta -12=0\Rightarrow \cos \theta =\cos \alpha =\frac{-4}{5},\frac{3}{5}$
Since, $\frac{\pi }{2}<\alpha <\pi$ $,\cos \alpha =\frac{-4}{5}\sin \alpha =\sqrt{1-(\frac{-4}{5}{)}^2}=\frac{3}{5}$
Now, $\sin 2\alpha =2\sin \alpha \cos \alpha =2\ast \frac{3}{5}\ast \frac{-4}{5}=\frac{-24}{25}$