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