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Let $n$ be a nonnegative integer. Can you help me prove the following ?

There exists a unique polynomial $P_{n}$ such that for all $t \in [0,\frac{\pi}{2}]$, $P_{n}(\operatorname{cotan}^2t)=\frac{\sin((2n+1)t}{(\sin t)^{2n+1}}$ with $\operatorname{cotan}(x)=\frac{\cos x}{\sin x}$.

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    Where are you stuck? For the existence or the uniqueness?2012-01-11
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    For the moment, both, but I guess the hardest part is proving the uniqueness.2012-01-11

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