Write the given expression as the sine of an angle. $\sin 85 ^ { \circ } \cos 50 ^ { \circ } + \sin 50 ^ { \circ } \cos 85 ^ { \circ }$
A) $\sin \left( - 100 ^ { \circ } \right)$
B) $\sin \left( 135 ^ { \circ } \right)$
C) $\sin \left( 35 ^ { \circ } \right)$
D) $\sin \left( 85 ^ { \circ } \right)$
E) $\sin \left( 50 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

This expression can be simplified using the sine addition formula, $\sin(A + B) = \sin A \cos B + \cos A \sin B$, which directly matches the given expression with $A = 85^\circ$ and $B = 50^\circ$. Therefore, the expression simplifies to $\sin(85^\circ + 50^\circ) = \sin(135^\circ)$.

Write the Given Expression as the Sine of an Angle sin⁡85∘cos⁡50∘+sin⁡50∘cos⁡85∘\sin 85 ^ { \circ } \cos 50 ^ { \circ } + \sin 50 ^ { \circ } \cos 85 ^ { \circ }sin85∘cos50∘+sin50∘cos85∘

Write the Given Expression as the Sine of an Angle $\sin 85 ^ { \circ } \cos 50 ^ { \circ } + \sin 50 ^ { \circ } \cos 85 ^ { \circ }$