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Prove that sum(r=0)^(n) ""^(n)C(r )sin ...

Prove that `sum_(r=0)^(n) ""^(n)C_(r )sin rx. cos (n-r)x = 2^(n-1) xx sin nx`.

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To prove that \[ \sum_{r=0}^{n} \binom{n}{r} \sin(rx) \cos((n-r)x) = 2^{n-1} \sin(nx), \] we will follow these steps: ...
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