Write the given expression as the cosine of an angle. $\cos 30 ^ { \circ } \cos 50 ^ { \circ } + \sin 30 ^ { \circ } \sin 50 ^ { \circ }$
A) $\cos \left( 50 ^ { \circ } \right)$
B) $\cos \left( - 20 ^ { \circ } \right)$
C) $\cos \left( 80 ^ { \circ } \right)$
D) $\cos \left( 30 ^ { \circ } \right)$
E) $\cos \left( - 100 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

Using the sum-to-product formula for cosine, we have:$\cos 30 ^ { \circ } \cos 50 ^ { \circ } + \sin 30 ^ { \circ } \sin 50 ^ { \circ } = \cos (50 ^ { \circ } - 30 ^ { \circ }) = \cos 20 ^ { \circ } = \cos (-20 ^ { \circ })$

Write the Given Expression as the Cosine of an Angle cos⁡30∘cos⁡50∘+sin⁡30∘sin⁡50∘\cos 30 ^ { \circ } \cos 50 ^ { \circ } + \sin 30 ^ { \circ } \sin 50 ^ { \circ }cos30∘cos50∘+sin30∘sin50∘

Write the Given Expression as the Cosine of an Angle $\cos 30 ^ { \circ } \cos 50 ^ { \circ } + \sin 30 ^ { \circ } \sin 50 ^ { \circ }$