AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(3 a=b+c\), then \(\cot \frac{B}{2} \cot \frac{C}{2}=\)
- A 1
- B 2
- C \(\frac{1}{3}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Let \(a, b, c\) are the sides of the \(\triangle A B C\) and \(s\) is the semi-perimeter \[ s=\frac{a+b+c}{2} \] Put the value of Eq. (i), we get \[ s=\frac{a+3 a}{2}=\frac{4 a}{2}=2 a \] Now, \(\cot \frac{B}{2} \cot \frac{C}{2}\)…
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