I was going through a question on finding the Fourier sine transform of the following function: $$\frac{e^{ax}+e^{-ax}}{e^{\pi x}-e^{-\pi x}}.$$
Attempt:
So I got stuck with the following integral: $$ \int_{0}^\infty \frac{e^{(a+ip)x}-e^{-(a+ip)x}dx}{e^{\pi x}-e^{-\pi x}} = \frac{1}{2} \tan {\frac{a+ip}{2}}$$
The second one which i guess must be quite similar to the former that I encountered in another similar question is:
$$\int_{0}^\infty \frac{e^{(a+ip)x}+e^{-(a+ip)x}dx}{e^{\pi x}-e^{-\pi x}} = \frac{1}{2} \sec {\frac{a+ip}{2}}$$
I am not able to understand how to proceed with these two. Any help would be appreciated.