Use identities to fill in the blank with the appropriate trigonometric function name.
-$$\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 2 }$$
A) $- 2 \cos \frac { 13 \pi } { 44 } \cos \left( \frac { - 9 \pi } { 44 } \right)$
B) $- 2 \sin \frac { 13 \pi } { 44 } \sin \left( \frac { - 9 \pi } { 44 } \right)$
C) $- 2 \sin \frac { 13 \pi } { 44 } \cos \left( \frac { - 9 \pi } { 44 } \right)$
D) $- 2 \cos \frac { 13 \pi } { 44 } \sin \left( \frac { - 9 \pi } { 44 } \right)$

Question

Quizplus · Accepted Answer

The identity for the difference of cosines is $\cos A - \cos B = -2 \sin \left( \frac{A+B}{2} \right) \sin \left( \frac{A-B}{2} \right)$. Applying this to $\cos \frac{\pi}{11} - \cos \frac{\pi}{2}$, we get $-2 \sin \frac{13\pi}{44} \sin \left( \frac{-9\pi}{44} \right)$.

Use Identities to Fill in the Blank with the Appropriate cos⁡π11−cos⁡π2\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 2 }cos11π​−cos2π​

Use Identities to Fill in the Blank with the Appropriate $\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 2 }$