Answer
$$4\sin\frac{\pi}{3}\cos\frac{\pi}{3}=\sqrt3$$
5 would be matched with F.
Work Step by Step
$$X=4\sin\frac{\pi}{3}\cos\frac{\pi}{3}$$
$$X=2\times(2\sin\frac{\pi}{3}\cos\frac{\pi}{3})$$
From the double-angle identities:
$$2\sin A\cos A=\sin2A$$
Thus $2\sin\frac{\pi}{3}\cos\frac{\pi}{3}$ can be seen here as $2\sin A\cos A$ with $A=\frac{\pi}{3}$.
Therefore,
$$X=2\times\Big[\sin\Big(2\times\frac{\pi}{3}\Big)\Big]$$
$$X=2\sin\frac{2\pi}{3}$$
$|\sin\frac{2\pi}{3}|=\sin\frac{\pi}{3}$. As $\frac{2\pi}{3}$ is in quadrant II, in which $\sin\theta\gt0$, so $\sin\frac{2\pi}{3}=\sin\frac{\pi}{3}=\frac{\sqrt3}{2}$.
$$X=2\times\frac{\sqrt3}{2}$$
$$X=\sqrt3$$
So, $$4\sin\frac{\pi}{3}\cos\frac{\pi}{3}=\sqrt3$$
5 would be matched with F.
