Rewrite the following as a product of trigonometric functions.
-$$\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 8 }$$
A) $- 2 \sin \frac { 19 \pi } { 176 } \sin \left( \frac { - 3 \pi } { 176 } \right)$
B) $- 2 \sin \frac { 19 \pi } { 176 } \cos \left( \frac { - 3 \pi } { 176 } \right)$
C) $- 2 \cos \frac { 19 \pi } { 176 } \sin \left( \frac { - 3 \pi } { 176 } \right)$
D) $- 2 \cos \frac { 19 \pi } { 176 } \cos \left( \frac { - 3 \pi } { 176 } \right)$

Question

Quizplus · Accepted Answer

The expression can be rewritten using the cosine subtraction formula, $\cos A - \cos B = -2 \sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)$. Applying this to $\cos \frac{\pi}{11} - \cos \frac{\pi}{8}$, we get $-2 \sin \left( \frac{\frac{\pi}{11} + \frac{\pi}{8}}{2} \right) \sin \left( \frac{\frac{\pi}{11} - \frac{\pi}{8}}{2} \right)$, which simplifies to choice A.

Rewrite the Following as a Product of Trigonometric Functions cos⁡π11−cos⁡π8\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 8 }cos11π​−cos8π​

Rewrite the Following as a Product of Trigonometric Functions $\cos \frac { \pi } { 11 } - \cos \frac { \pi } { 8 }$