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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