Puzzle Solving - How to Transform (eqn 1) to (eqn 2)?

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The discussion revolves around transforming the equation f(x) = f(x1)*f(x-x1) / [ (cot(x1) + cot(x-x1) ] into f(x) = 1 / (sin(x)). Participants express confusion about the transformation process and seek guidance on how to derive the second equation from the first. Clarifications are made regarding the variable x1, which can be any value within the specified range of 0 < x1 < x. The importance of precise mathematical language is emphasized, highlighting that every detail matters in mathematical discussions. Overall, the thread seeks a clear method for solving this mathematical puzzle.
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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 don't know how to start it.
 
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Can you check and make sure you wrote this down correctly.

Also, I assume x1 means x_1.

Also, x_1 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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