Question

In `DeltaABC, acos^(2)C/2+ccos^(2)A/2=(3b)/(2)`, then prove that the sides of `DeltaABC`, are in A.P.

Answer 1

`acos^(2)C/2+cos^(2)A/2=(3b)/(2)`
`rArr (a.(1+cosC))/(2)+(c.(1+cosA))/(2)=(3b)/(2)`
`rArr a(1+cosC)+c(1+cosA)=3b`
`rArr a+acosC+c+(c)cosA=3b`
`rArr a+c+(acosC+(c)cosA)=3b`
`rArr a+c+b=3b`
`rArr a+c+B=3b`
`rArr a+c=2b`
`rArr a+c=2b`
`rArr` a,b,c are in A.P. Hence Proved.