(eqn 1) f(x) = f(x1)*f(x-x1) / [ (cot(x1) + cot(x-x1) ]

an it continue that the solution to it is

(eqn 2) f(x) = 1 / (sin(x) ).

I admit that it is indeed easy to show that eqn 2 does fit to eqn 1 but I don't really have idea how to get eqn 2 out of eqn 1. Will anybody share their idea how to do this stuff? This puzzles me because it seems easy but I just dont know how to start it.