In $\triangle \mathrm{ABC}$, if a $\cos ^2 \frac{\mathrm{C}}{2}+\cos ^2 \frac{\mathrm{A}}{2}=\frac{3…

In $\triangle \mathrm{ABC}$, if a $\cos ^2 \frac{\mathrm{C}}{2}+\cos ^2 \frac{\mathrm{A}}{2}=\frac{3 \mathrm{~b}}{2}$, then $\mathrm{a}+\mathrm{c}: \mathrm{b}=$
  1. $1: 1$
  2. $3: 2$
  3. $2: 1$
  4. $4: 3$

Solution

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

Asked in: AP EAMCET 2023 (15 May Shift 2)

Practice more Trigonometric Functions questions on Aicharya