The Cosine Product!

Geometry Level 2

f(x)=cos(x)cos(2x)cos(3x)cos(999x)\large f(x) = \cos(x) \cdot \cos(2x) \cdot \cos(3x)\cdots \cos(999x)

If f(2π1999)=12kf \left(\dfrac{2\pi }{1999}\right) = \dfrac{1}{2^{k}}, find kk.

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