Use a sum or difference identity to find the exact value.
-$\sin \frac { 7 \pi } { 24 } \cos \frac { \pi } { 8 } - \cos \frac { 7 \pi } { 24 } \sin \frac { \pi } { 8 }$
A) $\frac { 1 } { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) 1
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression can be simplified using the sine difference identity, $\sin(a - b) = \sin a \cos b - \cos a \sin b$. Applying this identity with $a = \frac{7\pi}{24}$ and $b = \frac{\pi}{8}$, we get $\sin(\frac{7\pi}{24} - \frac{\pi}{8}) = \sin(\frac{7\pi}{24} - \frac{3\pi}{24}) = \sin(\frac{4\pi}{24}) = \sin(\frac{\pi}{6})$, which equals $\frac{1}{2}$.

Use a Sum or Difference Identity to Find the Exact sin⁡7π24cos⁡π8−cos⁡7π24sin⁡π8\sin \frac { 7 \pi } { 24 } \cos \frac { \pi } { 8 } - \cos \frac { 7 \pi } { 24 } \sin \frac { \pi } { 8 }sin247π​cos8π​−cos247π​sin8π​

Use a Sum or Difference Identity to Find the Exact $\sin \frac { 7 \pi } { 24 } \cos \frac { \pi } { 8 } - \cos \frac { 7 \pi } { 24 } \sin \frac { \pi } { 8 }$