Q67 / 160 · AP EAMCET 2023 (15 May Shift 2) · Mathematics

In $\triangle \mathrm{ABC}$, if a $\cos ^2 \frac{\mathrm{C}}{2}+\cos ^2 \frac{\mathrm{A}}{2}=\frac{3 \mathrm{~b}}{2}$, then $\mathrm{a}+\mathrm{c}: \mathrm{b}=$

  • A
    $1: 1$
  • B
    $3: 2$
  • Correct answer
    C
    $2: 1$
  • D
    $4: 3$

Solution

$\begin{aligned} & \text {Given } a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2} \\ & \Rightarrow \frac{a(1+\cos C)+c(1+\cos A)}{2}=\frac{3 b}{2} \\ & \Rightarrow a+c+a \cos C+c \cos A=3 b \\ & \Rightarrow a+c+b=3 b \Rightarrow \frac{a+c}{b}=\frac{2}{1}\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions