Find the Exact Value by Using a Half-Angle Identity $$\cos \frac { 5 \pi } { 12 }$$

Find the exact value by using a half-angle identity.
- $$\cos \frac { 5 \pi } { 12 }$$

A) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
B) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$
C) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$
D) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$