Find the exact value. $\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }$
A) $\frac { 3 \sqrt { 2 } } { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) $1$
D) $- \frac { \sqrt { 3 } } { 2 }$
E) none

Question

Quizplus · Accepted Answer

We recognize that $\cos(95^\circ)$ is the same as $\sin(5^\circ)$ and that $\cos(50^\circ)$ is the same as $\sin(40^\circ)$. Then we have:
\begin{align*}
\cos(95^\circ)\cos(50^\circ)+\sin(95^\circ)\sin(50^\circ)&=\sin(5^\circ)\sin(40^\circ)+\cos(5^\circ)\cos(40^\circ)\
&=\cos(40^\circ-5^\circ)=\cos(35^\circ)\
&=\cos(45^\circ-10^\circ)\
&=\frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}+1}{2}\
&=\boxed{\frac{\sqrt{2}}{2}}
\end{align*}

Find the Exact Value cos⁡95∘cos⁡50∘+sin⁡95∘sin⁡50∘\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }cos95∘cos50∘+sin95∘sin50∘

Find the Exact Value $\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }$