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Properties of Triangles (This question is based on Properties of Triangles), Prove that in a triangle ABC, a^3 . cos(B-C) + b^3 . cos(C-A) + c^3 . cos(A-B) = 3abc.

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Prove that in a triangle ABC,
                   a^3 . cos(B-C) + b^3 . cos(C-A) + c^3 . cos(A-B) = 3abc.
[IIT 1970;   IC 1983]

 SOLUTION : 

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