AP EAMCET · Maths · Properties of Triangles
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 \(3: 2\)
- C \(2: 1\)
- D \(4: 3\)
Answer & Solution
Correct Answer
(C) \(2: 1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Given } a \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2} \\ & \Rightarrow \frac{a(1+\cos C)+c(1+\cos A)}{2}=\frac{3 b}{2} \\ & \Rightarrow a+c+a \cos C+c \cos A=3 b \\ & \Rightarrow a+c+b=3 b \Rightarrow \frac{a+c}{b}=\frac{2}{1}\end{aligned}\)
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