Use the Half-Angle Formulas to Simplify the Expression $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

Multiple Choice

Use the half-angle formulas to simplify the expression. $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

A) $- \left| \sin \left( \frac { x - 3 } { 2 } \right) \right|$
B) $- \left| \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right) \right|$
C) $- | \sin ( x - 3 ) |$
D) $- \left| \sin ^ { - 1 } \left( \frac { x - 3 } { 2 } \right) \right|$
E) $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$