To simplify the given trigonometric equation, we can use the product-to-sum identities:

sin A sin B = 0.5$$cos(A-B)-cos(A+B)$$

Applying this identity to both sides of the equation, we get:

0.5$$cos(x-11x)-cos(x+11x)$$ = 0.5$$cos(3x-9x)-cos(3x+9x)$$

Simplifying both sides:

0.5$$cos(-10x)-cos(12x)$$ = 0.5$$cos(-6x)-cos(12x)$$

cos$-\theta$ = cos$\theta$, so we get:

0.5$$cos(10x)-cos(12x)$$ = 0.5$$cos(-6x)-cos(12x)$$

cos$\theta$ - cos$\phi$ = 2 sin$0.5(\theta +\phi )$ sin$0.5(\theta -\phi )$, so:

2 sin$0.5(10x-12x)$ sin$0.5(10x+12x)$ = 2 sin$0.5(-6x-12x)$ sin$0.5(-6x+12x)$

sin$-\theta$ = -sin$\theta$, so by simplifying further, we get:

2 sin$-x$ sin$11x$ = 2 sin$-9x$ sin$3x$

-2 sin$x$ sin$11x$ = -2 sin$9x$ sin$3x$

sin$x$ sin$11x$ = sin$9x$ sin$3x$

Therefore, the simplified form of the given trigonometric equation is sin$x$ sin$11x$ = sin$9x$ sin$3x$.