Question

In Triangle ABC , Prove that
b=a cosC+c CosB​

Answer 1

Answer:

L.H.S.

a(bcosC−ccosB)

=abcosC−accosB

Using cosine formula

cosC=

2ab

a

2

+b

2

−c

2

and cosB=

2ac

a

2

+c

2

−b

2

Then,

=ab(

2ab

a

2

+b

2

−c

2

)−ac(

2ac

a

2

+c

2

−b

2

)

=

2

a

2

+b

2

−c

2

−a

2

−c

2

+b

2

=

2

2(b

2

−c

2

)

=b

2

−c

2