Question

Solve: $\sin \left\{2{\cos }^{-1}\left(-\frac{3}{5}\right)\right\}$

Answer 1

Let $\theta ={\cos }^{-1}\left(\frac{-3}{5}\right)$

$\Rightarrow \cos \theta =-\frac{3}{5}$

So,$\theta$ lies in $2^{nd}$ or $3^{rd}$ quadrant.

$\Rightarrow \sin \theta =\pm \frac{4}{5}$

Now $\sin 2\theta =2\sin \theta \cos \theta$

$=2(\pm \frac{4}{5})(-\frac{3}{5})=\pm \frac{24}{25}$