Write the expression as the sine, cosine, or tangent of an angle.
-$\cos \frac { \pi } { 7 } \cos \frac { \pi } { 11 } + \sin \frac { \pi } { 7 } \sin \frac { \pi } { 11 }$
A) $\sin \frac { 18 \pi } { 77 }$
B) $\cos \frac { 4 \pi } { 77 }$
C) $\sin \frac { 4 \pi } { 77 }$
D) $\cos \frac { 18 \pi } { 77 }$

Question

Quizplus · Accepted Answer

This expression can be simplified using the cosine of a sum formula, $\cos(A + B) = \cos A \cos B + \sin A \sin B$. Applying this formula, the expression simplifies to $\cos \left( \frac{\pi}{7} + \frac{\pi}{11} \right)$, which equals $\cos \frac{4\pi}{77}$.

Write the Expression as the Sine, Cosine, or Tangent of an Angle