Use a sum-to-product identity to rewrite the expression.
-sin 43° + sin 55°
A) -2 sin 49° sin 6°
B) 2 cos 49° cos 6°
C) 2 sin 49° cos 6°
D) 2 cos 49° sin 6°

Question

Quizplus · Accepted Answer

The sum-to-product identity for sine is given by $\sin A + \sin B = 2 \sin \left(\frac{A + B}{2}\right) \cos \left(\frac{A - B}{2}\right)$. Applying this to $\sin 43° + \sin 55°$, we get $2 \sin \left(\frac{43° + 55°}{2}\right) \cos \left(\frac{43° - 55°}{2}\right) = 2 \sin 49° \cos 6°$.

Use a Sum-To-Product Identity to Rewrite the Expression