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) = cotB
drwls and I have answered about 5 of your questions based on the same type of trig expansions.
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