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

In `DeltaABC, acos^(2)C/2+ccos^(2)A/2=(3b)/(2)`, then prove that the s

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