Write the given expression as the sine of an angle. $\sin 75 ^ { \circ } \cos 35 ^ { \circ } - \sin 35 ^ { \circ } \cos 75 ^ { \circ }$
A) $\sin \left( - 70 ^ { \circ } \right)$
B) $\sin \left( 40 ^ { \circ } \right)$
C) $\sin \left( 110 ^ { \circ } \right)$
D) $\sin \left( 75 ^ { \circ } \right)$
E) $\sin \left( 35 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

Using the formula for the difference of sines of angles, we get:
$$\sin (A - B) = \sin A \cos B - \cos A \sin B$$
So,
\begin{align*}
\sin 75^{\circ} \cos 35^{\circ} - \sin 35^{\circ} \cos 75^{\circ} &= \sin (75^{\circ} - 35^{\circ}) \
&= \sin 40^{\circ}
\end{align*}

Write the Given Expression as the Sine of an Angle sin⁡75∘cos⁡35∘−sin⁡35∘cos⁡75∘\sin 75 ^ { \circ } \cos 35 ^ { \circ } - \sin 35 ^ { \circ } \cos 75 ^ { \circ }sin75∘cos35∘−sin35∘cos75∘

Write the Given Expression as the Sine of an Angle $\sin 75 ^ { \circ } \cos 35 ^ { \circ } - \sin 35 ^ { \circ } \cos 75 ^ { \circ }$