Use Sum and Difference Formulas for Cosines and Sines
-$\cos \frac { 7 \pi } { 12 } \sin \frac { 5 \pi } { 12 } - \cos \frac { 5 \pi } { 12 } \sin \frac { 7 \pi } { 12 }$
A) $\frac { 1 } { 2 }$
B) $\frac { \sqrt { 3 } } { 2 }$
C) $\frac { 1 } { 4 }$
D) 1

Question

Quizplus · Accepted Answer

The expression is equivalent to $\sin\left(\frac{7\pi}{12} - \frac{5\pi}{12}\right)$, which simplifies to $\sin\left(\frac{2\pi}{12}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$.

Use Sum and Difference Formulas for Cosines and Sines - cos⁡7π12sin⁡5π12−cos⁡5π12sin⁡7π12\cos \frac { 7 \pi } { 12 } \sin \frac { 5 \pi } { 12 } - \cos \frac { 5 \pi } { 12 } \sin \frac { 7 \pi } { 12 }cos127π​sin125π​−cos125π​sin127π​

Use Sum and Difference Formulas for Cosines and Sines
- $\cos \frac { 7 \pi } { 12 } \sin \frac { 5 \pi } { 12 } - \cos \frac { 5 \pi } { 12 } \sin \frac { 7 \pi } { 12 }$