Answer
$$2\sin22.5^\circ\cos22.5^\circ=\frac{\sqrt2}{2}$$
We match 3 with B.
Work Step by Step
$$X=2\sin22.5^\circ\cos22.5^\circ$$
Recall the double-angle identities:
$$2\sin A\cos A=\sin2A$$
$X$ can be seen here as $2\sin A\cos A$ with $A=22.5^\circ$.
Therefore,
$$X=2\sin22.5^\circ\cos22.5^\circ=\sin(2\times22.5^\circ)$$
$$X=\sin45^\circ$$
$$X=\frac{\sqrt2}{2}$$
So, $$2\sin22.5^\circ\cos22.5^\circ=\frac{\sqrt2}{2}$$
3 would come with B.
