Question

show that in any triangle ABC, c=a(cosB) + b(cosA)
(Hint: consider separately the cases where both A and B are acute and where one of them is obtuse.)

Answer 1

@mathmetics your question is wrong OR you have typed it wrong question ?

The original question is :-
Prove that in triangle ABC :-
\[\large \bf cosC=aCosB+bcosA\]

Answer 2

hmmmm....... it is what it says on the proble
may be problem is wrong... thx anyway

Answer 3

You need to use the law of cosines such that:







Substituting for and for yields:





Reducing duplicate factors, yields:



Bringing both sides to a common denominator, yields:



Reducing duplicate terms and , to the right side, yields:



Hence, testing if the expression holds, using the law of cosines, yields that is a valid expression.