I would be very grateful if someone could help me with my proof. I want to show that

where

Cn is a constant. I begin by squaring the above equation, getting:

Simplifying this equation gives:

Next I integrate. Perhaps an expert in trigonometry might spot other ways of reducing the above equation

It is during the integration of this above equation that I'm having my difficulty. I can integrate the first four terms and the second last term but I'm very unsure about the integrals with hyperbolic functions. Can anyone help me?

I see that my equations have appeared very small, but if you click on them, they will be bigger and easier to read. I hope this doesn't put people off