sin^2 (π/8 + x/2) - sin^2 (π/8 - x/2) = sin π/4 sin x = 1/√2 sinx

Question

Prove that:

^{\(sin^2(\frac{\pi}{8} + \frac{x}{2}) - sin^2(\frac{\pi}{8} - \frac{x}{2}) = sin \frac{\pi}{4} \ sin \ x = \frac{1}{\sqrt2} \ sinx\)}

Answer 1

= sin \(\frac{\pi}{4}.\) sin x = \(\frac{1}{\sqrt2}\) sin x = R.H.S. Hence Proved