Find the exact value under the given conditions.
-$\sin \left( \frac { - 5 \pi } { 6 } - \alpha \right) \cos \left( \frac { - 5 \pi } { 6 } + \alpha \right) + \cos \left( \frac { - 5 \pi } { 6 } - \alpha \right) \sin \left( \frac { - 5 \pi } { 6 } + \alpha \right)$
A) $\frac { \sqrt { 3 } } { 2 }$
B) $- \frac { 1 } { 2 }$
C) $\frac { 1 } { 2 }$
D) $- \frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

Using the sum and difference identities for sine and cosine, we have:$\sin \left( \frac { - 5 \pi } { 6 } - \alpha \right) \cos \left( \frac { - 5 \pi } { 6 } + \alpha \right) + \cos \left( \frac { - 5 \pi } { 6 } - \alpha \right) \sin \left( \frac { - 5 \pi } { 6 } + \alpha \right)$$= \sin \left( \frac { - 5 \pi } { 6 } - \alpha + \frac { - 5 \pi } { 6 } + \alpha \right)$$= \sin \left( - \frac { 5 \pi } { 3 } \right)$$= \sin \left( \frac { \pi } { 3 } \right)$$= \frac { \sqrt { 3 } } { 2 }$

Find the Exact Value Under the Given Conditions A) 32\frac { \sqrt { 3 } } { 2 }23​​

Find the Exact Value Under the Given Conditions A) $\frac { \sqrt { 3 } } { 2 }$