Question

Prove that cos2 2x – cos2 6x = sin 4x sin 8x

Answer 1

\(cos^2(2x) - cos^2(6x) = sin(4x)sin(8x)\)

Hint: There are two identities you need:
1. Power reduction: \(\large{cos^2(\theta) = \frac{1+cos(2\theta)}{2}}\)
2. Product-to-sum identity: \(\large{sin(x)sin(y) = \frac{1}{2} (cos(x - y) - cos(x + y))}\)