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

Multiple Choice

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

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