Question

In $ABC$, lf $aCo{s}^2\frac{C}{2}+cCo{s}^2\frac{A}{2}=\frac{3b}{2}$, then $a,b,c$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is A A.P.

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

$a\cos C+c\cos A=3b-a-c$

$b=3b-a-c$

$\frac{a+c}{2}=b$

$\therefore$ a, b, c, are in AP.

$(b=a\cos C+c\cos A)$