Use a product-to-sum identity to rewrite the expression.
-sin(17s - 2) sin (4s - 5)
A) 0.5(sin(13s + 3) - sin(21s - 7))
B) 0.5(cos(13s - 7) - cos(21s - 3))
C) 0.5(cos(13s + 3) + cos(21s - 7))
D) 0.5(cos(13s + 3) - cos(21s - 7))

Question

Quizplus · Accepted Answer

The product-to-sum identity for sine functions is given by $\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$. Applying this to $\sin(17s - 2) \sin (4s - 5)$, we get $A = 17s - 2$ and $B = 4s - 5$. Thus, $A - B = 13s + 3$ and $A + B = 21s - 7$, leading to the correct expression $\frac{1}{2}(\cos(13s + 3) - \cos(21s - 7))$.

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