SOLUTION: If cos(A-B)+cos(B-C)+cos(C-A)= -3/2, prove that: cosA+cosB+cosC=sinA+sinB+sinC=0.

SOLUTION: If cos(A-B)+cos(B-C)+cos(C-A)= -3/2, prove that: cosA+cosB+cosC=sinA+sinB+sinC=0.

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Question 1046271: If cos(A-B)+cos(B-C)+cos(C-A)= -3/2, prove that: cosA+cosB+cosC=sinA+sinB+sinC=0.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Consider
=

=.
But ===> .
Since the values of A, B, and C are real, all the sine and cosine values are also real, and so, we conclude that
and , hence
cosA+cosB+cosC = 0 and sinA+sinB+sinC = 0.
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