Answer
$2\sin^2(3x)=1-\cos(6x)$
Work Step by Step
Start with the right side:
$1-\cos(6x)$
Rewrite $6x$ as $2*3x$:
$=1-\cos(2*3x)$
Use the Double-Angle Formula $\cos 2u=1-2\sin^2 u$ where $u=3x$:
$=1-(1-2\sin^2(3x))$
$=2\sin^2(3x))$
Since this equals the left side, the identity has been proven.
