question 8 of 10 cos(x/5)sin(x/5)=1/2sin(2x/5) a. true b. false

Answer:

A. True

Explanation:

Step1: Recall double - angle formula

The double - angle formula for sine is $\sin(2\alpha)=2\sin\alpha\cos\alpha$, or $\sin\alpha\cos\alpha=\frac{1}{2}\sin(2\alpha)$.

Step2: Substitute $\alpha=\frac{x}{5}$

Let $\alpha = \frac{x}{5}$. Then $\cos(\frac{x}{5})\sin(\frac{x}{5})=\frac{1}{2}\sin(2\times\frac{x}{5})=\frac{1}{2}\sin(\frac{2x}{5})$.