To prove that sin(x/2) * cos(x/2) = 1/2, we can use the double angle formula for sine:

sin(2θ) = 2sinθcosθ

Let's substitute θ with x/2:

sin(x) = 2sin(x/2)cos(x/2)

Now, let's divide both sides of the equation by 2:

sin(x)/2 = sin(x/2)cos(x/2)

Since sin(x)/2 = 1/2, we can substitute it in the equation:

1/2 = sin(x/2)cos(x/2)

Therefore, sin(x/2) * cos(x/2) = 1/2.