sin(x/2)cos(x/2)cos(x) can be simplified using the double angle trigonometric identity:

cos(2θ) = 2cos^2(θ) - 1

We can rewrite sin(x/2)cos(x/2)cos(x) as sin(x/2)cos(x/2)cos(x) = 1/2sin(x)cos(x) = 1/2sin(2x)

Therefore, sin(x/2)cos(x/2)cos(x) simplifies to 1/2sin(2x)