# Cosine Last Year, Sine Next Year

Algebra Level 5

If $$\cos (2013 x)$$ is stated in terms of a polynomial of $$\cos (x)$$, the coefficient of $$\cos^{2013} (x)$$ is equals to $$A \cdot 2^B$$

And if $$\sin (2015 x)$$ is stated in terms of a polynomial of $$\sin (x)$$, the coefficient of $$\sin^{2015} (x)$$ is equals to $$C \cdot 2^D$$

Where $$A, B, C, D$$ are integers, with $$A$$ and $$C$$ as odd numbers. What is the value of $$(A+B)-(C+D)$$?

Details and assumptions:

• As an explicit example: if $$\cos(3x)$$ is stated in terms of a polynomial of $$\cos(x)$$, it would be $$4 \cos^3 (x) - 3\cos (x)$$
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