question 2 of 10 sin(x/7)sin(x/7)=1/21 - cos(2x/7) a. true b. false

Answer:

A. True

Explanation:

Step1: Recall double - angle formula

We know the double - angle formula for cosine: $\cos(2\alpha)=1 - 2\sin^{2}\alpha$. Rearranging it gives $\sin^{2}\alpha=\frac{1}{2}[1 - \cos(2\alpha)]$.

Step2: Substitute $\alpha=\frac{x}{7}$

Let $\alpha = \frac{x}{7}$. Then $\sin\left(\frac{x}{7}\right)\sin\left(\frac{x}{7}\right)=\sin^{2}\left(\frac{x}{7}\right)$. And using the formula $\sin^{2}\alpha=\frac{1}{2}[1 - \cos(2\alpha)]$ with $\alpha=\frac{x}{7}$, we get $\sin^{2}\left(\frac{x}{7}\right)=\frac{1}{2}\left[1-\cos\left(\frac{2x}{7}\right)\right]$.