# What's this function?

Geometry Level 4

$\large \displaystyle \sum^{n}_{r=0} {^{n}C_{r} \sin(rx) \cos((n-r)x)=f(n)\sin(nx)}$

Let $$f(n)$$ denote a function such that the equation above is an identity.

Find the value of $$f(15)$$.

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