AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C, \tan \frac{A}{2}+\tan \frac{B}{2}=\)
- A \(\frac{\cot \frac{C}{2}}{4 s}\)
- B \(\frac{2 c \cot \frac{c}{2}}{a+b+c}\)
- C \(\frac{2 c \tan \frac{C}{2}}{s}\)
- D \(\frac{c \tan \frac{c}{2}}{a+b+c}\)
Answer & Solution
Correct Answer
(B) \(\frac{2 c \cot \frac{c}{2}}{a+b+c}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)=\frac{\Delta}{s(s-a)}+\frac{\Delta}{s(s-b)} \\ & =\frac{\Delta}{s}\left\{\frac{1}{s-a}+\frac{1}{s-b}\right\}=\frac{c \Delta}{s(s-a)(s-b)} \\ & =\frac{2 c \Delta}{(a+b+c)(s-a)(s-b)} \\ & =\frac{2…
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