Question

Ex.(8) In AABC, prove that (a + b) cos C + (b + c) cosA +(c + a) cos B = a +b+c
Solution :​

Answer 1

Answer:- projection formulas of properties of traingle :

a cosB + b cosA = c

a cosC + c cosA = b  

b cosC + c cosB = a

To Prove:- (a + b) cos C + (b + c) cosA +(c + a) cos B = a +b+c

L.H.S.    (a+b) cosC + (c+a) cosB + (c+a) cosC

=> (a cosB +b cosA) + (a cosC+c cosA) + (b cosC + c cosB)

=> a+b+c = R.H.S.

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