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

Question

Quizplus · Accepted Answer

This expression can be simplified using the sine difference formula: $\sin(A - B) = \sin A \cos B - \cos A \sin B$. Applying this formula, the given expression simplifies to $\sin(85^\circ - 50^\circ) = \sin(35^\circ)$, which matches choice C.

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 $\sin 85 ^ { \circ } \cos 50 ^ { \circ } - \sin 50 ^ { \circ } \cos 85 ^ { \circ }$