Puzzling Equation

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I am reading an article that shows this equation

(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.
Can you check and make sure you wrote this down correctly.

Also, I assume x1 means [itex]x_1[/itex].

Also, [itex]x_1[/itex] can be anything I want?

Every detail to a question is important. There is no such thing as text talk in mathematics. ;)
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Im sorry for the incomplete information.

0< x_1 < x is the additional restriction.

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