Use the Half-Angle Formulas to Determine the Exact Value of the Following

Multiple Choice

Use the half-angle formulas to determine the exact value of the following.
$$\cos \left( 22.5 ^ { \circ } \right)$$

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