Write the given expression as the cosine of an angle. $$\cos 45 ^ { \circ } \cos 40 ^ { \circ } + \sin 45 ^ { \circ } \sin 40 ^ { \circ }$$
A) $\cos \left( 45 ^ { \circ } \right)$
B) $\cos \left( 5 ^ { \circ } \right)$
C) $\cos \left( - 80 ^ { \circ } \right)$
D) $\cos \left( 40 ^ { \circ } \right)$
E) $\cos \left( 85 ^ { \circ } \right)$

Question

Write the given expression as the cosine of an angle.​ $$\cos 45 ^ { \circ } \cos 40 ^ { \circ } + \sin 45 ^ { \circ } \sin 40 ^ { \circ }$$
A) $\cos \left( 45 ^ { \circ } \right)$
B) $\cos \left( 5 ^ { \circ } \right)$
C) $\cos \left( - 80 ^ { \circ } \right)$
D) $\cos \left( 40 ^ { \circ } \right)$
E) $\cos \left( 85 ^ { \circ } \right)$

Quizplus · Accepted Answer

The given expression is an application of the cosine addition formula: $\cos(A)\cos(B) + \sin(A)\sin(B) = \cos(A - B)$. Substituting $A = 45^\circ$ and $B = 40^\circ$, we get $\cos(45^\circ - 40^\circ) = \cos(5^\circ)$.

Write the Given Expression as the Cosine of an Angle cos⁡45∘cos⁡40∘+sin⁡45∘sin⁡40∘\cos 45 ^ { \circ } \cos 40 ^ { \circ } + \sin 45 ^ { \circ } \sin 40 ^ { \circ }cos45∘cos40∘+sin45∘sin40∘

Write the Given Expression as the Cosine of an Angle $\cos 45 ^ { \circ } \cos 40 ^ { \circ } + \sin 45 ^ { \circ } \sin 40 ^ { \circ }$