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.

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 :