Question

Prove sin(8x)sin(2x)=(sin(5x))^2-(sin(3x))^2

Answer 1

$$\begin{align*}
\sin(8x)\sin(2x) &= \frac 12 [\cos(6x)-\cos(10x)]\\
&=\frac 12 [1-2\sin^2(3x)-1+2\sin^2(5x)]\\
&=\frac 12[2\sin^2(5x)-2\sin^2(3x)]\\
&=\sin^2(5x)-\sin^2(3x)
\end{align*}$$

Answer 2

Yep thanks

Answer 3

\[\sin ^{2}A-\sin ^{2}B=\sin \left( A+B \right)\sin \left( A-B \right)\]