LHS = a cos A+ 6 cos B + c cos C
Using sine formula, we get k sin A cos A + k sin B cos B + k sin C cos C k
= (k/2) [2 sin A cos A + 2 sin B cos B + 2 sin C cos C]
= (k/2) [sin 2A + sin 2B + sin 2C]
= (k/2) [2 sin (A + B) . cos (A – B) + 2 sin C . cos C]
= (k/2) [2 sin (A – B) . cos (A – B) + 2 sin C . cos C]
= (k/2) [2 sin C . cos (A – B) + 2 sin C . cos C]
= k sin C [cos(A – B) + cos C]
= k sin C[cos(A - B) + cos(π - bar(A + B))
= k sin C [cos (A – B) – cos (A + B)]
= k sin C . 2 sin A sin B
= 2k sin A . sin B sin C
= 2a sin B sin C = RHS