To find f'(Π/6), we first need to find the derivative of the function f(x) with respect to x.

Given f(x) = (1 + sinx) / cosx

Using quotient rule, the derivative of f(x) is:

f'(x) = [cosx(0) - (1 + sinx)(-sinx)] / cos^2x
f'(x) = sinx / cos^2x

Now, we need to find f'(Π/6):

f'(Π/6) = sin(Π/6) / cos^2(Π/6)
f'(Π/6) = (√3 / 2) / (cos^2(Π/6))
f'(Π/6) = (√3 / 2) / (1/4)
f'(Π/6) = (√3 / 2) * 4
f'(Π/6) = 2√3

Therefore, f'(Π/6) = 2√3.