Fourier Transform deduce the following transform pair

1. Nov 4, 2015

grandpa2390

1. The problem statement, all variables and given/known data
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)

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

3. 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.

2. Nov 4, 2015

blue_leaf77

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