Prove that: `(cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C`

Explanation

To prove the identity:

\[ \frac{\cos(A+B+C) + \cos(-A+B+C) + \cos(A-B+C) + \cos(A+B-C)}{\sin(A+B+C) + \sin(-A+B+C) + \sin(A-B+C) - \sin(A+B-C)} = \cot C \]

we will use the sum-to-product identities for cosine and sine.

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