Write the given expression as the sine of an angle. $\sin 45 ^ { \circ } \cos 55 ^ { \circ } - \sin 55 ^ { \circ } 45 ^ { \circ }$
A) $\sin \left( - 110 ^ { \circ } \right)$
B) $\sin \left( - 10 ^ { \circ } \right)$
C) $\sin \left( 100 ^ { \circ } \right)$
D) $\sin \left( 45 ^ { \circ } \right)$
E) $\sin \left( 55 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the sine difference formula: $\sin(A - B) = \sin A \cos B - \cos A \sin B$. Applying this to the given expression, we get $\sin(45^\circ - 55^\circ) = \sin(-10^\circ)$, which matches choice B.

Write the Given Expression as the Sine of an Angle sin⁡45∘cos⁡55∘−sin⁡55∘45∘\sin 45 ^ { \circ } \cos 55 ^ { \circ } - \sin 55 ^ { \circ } 45 ^ { \circ }sin45∘cos55∘−sin55∘45∘

Write the Given Expression as the Sine of an Angle $\sin 45 ^ { \circ } \cos 55 ^ { \circ } - \sin 55 ^ { \circ } 45 ^ { \circ }$