#### Answer

$$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$
1 is matched with C.

#### Work Step by Step

$$X=2\cos^215^\circ-1$$
Recall the double-angle identities:
$$2\cos^2A-1=\cos2A$$
Here $X$ is like the form of $2\cos^2A-1$ with $A=15^\circ$. Therefore,
$$X=2\cos^215^\circ-1=\cos(2\times15^\circ)$$
$$X=\cos30^\circ$$
$$X=\frac{\sqrt3}{2}$$
So, $$2\cos^215^\circ-1=\frac{\sqrt3}{2}$$
We pick C here.