Now you will all point at me and laugh. I tried to prove that and all I get is
Where does it all go so wrong?
You've differentiated; you wanted to integrate. To integrate this, I would either write it as (and expand the brackets) or use some sort of double angle formula to manipulate.
You can also use the identity which I suspect Quacky was alluding to since (where a is a constant) are simple to integrate.
You get bonus kudos for deriving that identity yourself
Sure! By looking at the unit circle you can prove that and by substituting with this leads to . From these two formulae you can easily prove that and .