If A+B+C=2S then prove that cos (S-A) + cos (S-B) + cos (S-C) + cos S = 4 cos A/2 cos B/2 cos C/2.

Answer 1

See what you can do with your sum-to-product formulas. This should get you started:

cos(S-A)+cos(S)
= 2cos(((S-A)+S)/2)cos(((S-A)-S)/2)
= 2cos((2S-A)/2)cos(A/2)
= 2cos((B+C)/2)cos(A/2)

Answer 2

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