Question

In a $△ABC,c{\cos }^2\frac{A}{2}+a{\cos }^2\frac{C}{2}=\frac{3b}{2},$ then show that $a,b,c$ are in A.P

Answer 1

Here,$\frac{c}{2}(1+\cos A)+\frac{a}{2}(1+\cos C)=\frac{3b}{2}$

$a+c+b=3b$

$a+c=2b$

which shows $a+c=2b$