# Sum the products

Algebra Level 5

Let $$\displaystyle P(n)=\prod_{k=0}^{n} (\sin(k^\circ)+\cos(k^\circ))$$ and $$\displaystyle F(x)=\sum_{j=0}^{180} P(j) \cdot x^{j}$$. Find the degree of the polynomial $$F(x)$$.

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