To simplify sin(2x) * cos(2x), we can use the double angle identities for sine and cosine:

sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x)

Therefore, sin(2x) cos(2x) = (2sin(x)cos(x)) (cos^2(x) - sin^2(x)).

Expanding this expression, we get:

2sin(x)cos(x) cos^2(x) - 2sin(x)cos(x) sin^2(x)
= 2sin(x)cos(x) cos^2(x) - 2sin(x)cos(x) sin^2(x)
= 2sin(x)cos(x)cos^2(x) - 2sin(x)cos(x)sin^2(x)

Now, we can further simplify this expression using trigonometric identities:

2sin(x)cos(x)cos^2(x) = sin(x)2cos(x)cos^2(x) = sin(x)cos(x)2cos^2(x) = sin(x)cos(x)cos(2x)
2sin(x)cos(x)sin^2(x) = sin(x)2cos(x)sin^2(x) = sin(x)cos(x)2sin^2(x) = sin(x)cos(x)sin(2x)

Therefore, sin(2x) cos(2x) simplifies to sin(x)cos(x)cos(2x) - sin(x)cos(x)sin(2x) = sin(x)cos(x)cos(2x - 2x) = sin(x)cos(x)cos(0) = sin(x)cos(x) = 1/2 sin(2x).