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Harmony
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Question Statement
If A+B+C = 180, prove that cos (A+B-C) + cos (B+C-A) + cos (C+A-B) = 1+4 cosAcosBcosC
My Attempt
If A+B+C=180,
Then A+B-C=180-2C
cos (A+B-c)=cos(180-2C)
(After some substitution and caculation)
cos (A+B-C) = -cos 2C
Similarily, I obtain the same expression for cos (B+C-A), cos (C+A-B).
But that does not get me to the desire result.
Is my attempt wrong from the beginning?
If A+B+C = 180, prove that cos (A+B-C) + cos (B+C-A) + cos (C+A-B) = 1+4 cosAcosBcosC
My Attempt
If A+B+C=180,
Then A+B-C=180-2C
cos (A+B-c)=cos(180-2C)
(After some substitution and caculation)
cos (A+B-C) = -cos 2C
Similarily, I obtain the same expression for cos (B+C-A), cos (C+A-B).
But that does not get me to the desire result.
Is my attempt wrong from the beginning?