Fourier Transform deduce the following transform pair

[grandpa2390]

Homework Statement

I'm supposed to be using the similarity theorem and the shift theorem to solve:

cos(πx) / π(x-.5) has transform e^(-iπs)*Π(s)

Homework Equations

similarity theorem f(ax) has transform (1/a)F(s/a)
shift theorem f(x-a) has transform e^(-i2πas)F(s)

The Attempt at a Solution

I don't know. cos(πx) has the impulse pair transform and the impulse pair function has cos(πs) transform.
the only term that I can get is that the shift theorem will give me a e^(-iπs) because the 1/2 in the impulse function. I don't understand how to get the rect(s) term in the transform.

 

[blue_leaf77]

Use the fact that $\sin(\pi x - \frac{\pi}{2}) = -\cos(\pi x)$.