Use the Formula for the Cosine of the Difference of Two Angles
-$\cos \left( 160 ^ { \circ } \right) \cos \left( 40 ^ { \circ } \right) + \sin \left( 160 ^ { \circ } \right) \sin \left( 40 ^ { \circ } \right)$
A) $\cos \left( 120 ^ { \circ } \right)$
B) $\cos \left( 210 ^ { \circ } \right)$
C) $\cos \left( 190 ^ { \circ } \right)$
D) $\cos \left( 220 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The given expression is an application of the cosine difference identity, which is $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$. Applying this to the given angles, we get $\cos(160^\circ - 40^\circ) = \cos(120^\circ)$.