Given That $\cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2}$ , Find an Exact Expression For

Given that $\cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2}$ , find an exact expression for $\sin \left(\frac{\pi}{12}\right)$ .

A) $-\frac{\sqrt{2-\sqrt{3}}}{2}$
B) $-\frac{\sqrt{2+\sqrt{3}}}{2}$
C) $\frac{\sqrt{2-\sqrt{3}}}{2}$
D) $\frac{\sqrt{2+\sqrt{3}}}{2}$