TS EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(a+c=5 b\), then \(\cot \frac{A}{2} \cot \frac{C}{2}\) is equal to
- A 2
- B \(\frac{1}{2}\)
- C \(\frac{3}{2}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { LHS } \Rightarrow \cot \frac{A}{2} \cdot \cot \frac{C}{2}=\sqrt{\frac{s(s-a)}{(s-b)(s-c)}} \sqrt{\frac{s(s-c)}{(s-a)(s-b)}} \\ & =\sqrt{\frac{s(s-a)(s-c)}{(s-b)(s-c)(s-a)(s-b)}}=\frac{s}{s-b}=\frac{2 s}{2 s-2 b} \\ & =\frac{a+b+c}{a+b+c-2 b}=\frac{5…
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