Use the Formula for the Cosine of the Difference of Two Angles
-$\cos \left( \frac { 5 \pi } { 12 } \right) \cos \left( \frac { \pi } { 4 } \right) + \sin \left( \frac { 5 \pi } { 12 } \right) \sin \left( \frac { \pi } { 4 } \right)$
A) $\cos \left( \frac { \pi } { 6 } \right)$
B) $\cos \left( \frac { \pi } { 3 } \right)$
C) $\cos \left( \frac { 2 \pi } { 3 } \right)$
D) $\cos \left( \frac { 5 \pi } { 6 } \right)$ Find the exact value of the expression.

Question

Quizplus · Accepted Answer

The given expression is equivalent to the formula for the cosine of the difference of two angles, $\cos(A - B) = \cos A \cos B + \sin A \sin B$. Here, $A = \frac{5\pi}{12}$ and $B = \frac{\pi}{4}$, so the expression simplifies to $\cos\left(\frac{5\pi}{12} - \frac{\pi}{4}\right) = \cos\left(\frac{\pi}{6}\right)$.