Mark the tick against the correct answer in the following:

To Find: The value of $\sin \left(2 \sin ^{-1} \frac{4}{5}\right)$

Let, $x=\sin ^{-1} \frac{4}{5}$

$\Rightarrow \sin x=\frac{4}{5}$

We know that, $\cos x=\sqrt{1-\sin ^{2} x}$

$=\sqrt{1-\left(\frac{4}{5}\right)^{2}}$

$=\frac{3}{5}$

Now since, $x=\sin ^{-1} \frac{4}{5}$, hence $\sin \left(2 \sin ^{-1} \frac{4}{5}\right)$ becomes $\sin (2 x)$

Here, $\sin (2 x)=2 \sin x \cos x$

$=2 \times \frac{4}{5} \times \frac{3}{5}$

$=\frac{24}{25}$