# More Complex Than it Seems!

Algebra Level 5

$\large\sum_{r=0}^4 \dbinom4r b^{4-r} c^r \cos [ rB - (4-r)C ]$

Let $$a,b$$ and $$c$$ denote the sides of a triangle opposite to the angles $$A,B$$ and $$C$$ respectively.

Compute the value of the summation above, where $$a=5,b=12$$ and $$c=13$$.

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