Question

In any ΔABC, prove that:

(b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c.

Answer 1

LHS = (b + c) cos A + (c + a) cos B + (a + b) cos C

= b cos A + c cos A + c cos B + a cos B + a cos C + b cos C

= (b cos C + c cos B) + (a cos C + c cos A) + (a cos B + b cos A)

= a + b + c  ...[By projection rule]

= RHS.