To solve the equation sin(x)cos(5x) = sin(9x)cos(3x), we can use the trigonometric identity sin(a)cos(b) = 0.5sin(a+b) + 0.5*sin(a-b).

Applying this identity to the left side of the equation, we get:

0.5sin(x+5x) + 0.5sin(x-5x) = sin(6x) + sin(-4x)

And applying the identity to the right side of the equation, we get:

0.5sin(9x+3x) + 0.5sin(9x-3x) = sin(12x) + sin(6x)

Now, we have:

sin(6x) + sin(-4x) = sin(12x) + sin(6x)

Since sin(-θ) = -sin(θ), we get:

sin(6x) - sin(4x) = sin(12x) + sin(6x)

Now, rearrange the equation:

sin(6x) - sin(4x) - sin(6x) - sin(12x) = 0

-sin(4x) - sin(12x) = 0

Using sin addition rule, we can write the above equation as:

-2sin(8x)cos(4x) = 0

From here, we can see that the equation is true when either sin(8x) = 0 or cos(4x) = 0.

Therefore, this equation is satisfied when sin(8x) = 0 or cos(4x) = 0, which implies that x is a multiple of π/8 or π/4 respectively.