A colleague of mine came across this equation on an old exam: $$ \int_0^{\pi}{\cos n\theta\over\cos\theta-\cos\phi}\,d\theta={\pi\sin n\phi\over\sin\phi} $$ It said on the exam that students were allowed to assume this result.
My colleague (and I) would be much obliged if someone could present a reference to, or a proof of (or a refutation of), this formula. I suppose one is to assume $n$ is a positive integer.