Prove that: `sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2)sinA`

Explanation

To prove that \( \sin^2\left(\frac{\pi}{8} + \frac{A}{2}\right) - \sin^2\left(\frac{\pi}{8} - \frac{A}{2}\right) = \frac{1}{\sqrt{2}} \sin A \), we can use the identity for the difference of squares.

### Step-by-Step Solution:

1. **Use the Difference of Squares Identity:**
We know that:
\[
\sin^2 x - \sin^2 y = (\sin x + \sin y)(\sin x - \sin y)
...