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

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) ​ $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$

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