To find cos(a+b), we can use the sum of angles formula for cosine:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Given that sin(b) = 1/2 and a-b = π/2, we can solve for a:

a = b + π/2
a = π/2 + π/2
a = π

Now we can substitute the values of a and b into the formula for cos(a+b):

cos(π + 1/2) = cos(π)cos(1/2) - sin(π)sin(1/2)
cos(π + 1/2) = (-1)(√3/2) - 0(1/2)
cos(π + 1/2) = -√3/2

Therefore, cos(a+b) = -√3/2.