Find the exact value of the given expression. $$\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }$$
A) $\frac { 1 } { 2 }$
B) $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$
C) $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$
D) $\frac { \sqrt { 2 } } { 2 }$
E) $\frac { \sqrt { 3 } } { 2 }$

Question

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The Answer of Find the exact value of the given expression. $$\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }$$
A) $\frac { 1 } { 2 }$
B) $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$
C) $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$
D) $\frac { \sqrt { 2 } } { 2 }$
E) $\frac { \sqrt { 3 } } { 2 }$

Find the Exact Value of the Given Expression sin⁡105∘cos⁡345∘−sin⁡345∘cos⁡105∘\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }sin105∘cos345∘−sin345∘cos105∘

Find the Exact Value of the Given Expression $\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }$