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AP EAMCET · Maths · Properties of Triangles

In \(\triangle \mathrm{ABC},\left(\tan \frac{\mathrm{A}}{2}+\tan \frac{\mathrm{B}}{2}\right) \tan \frac{\mathrm{C}}{2}=\)

  1. A \(\frac{2 c}{a+b+c}\)
  2. B \(\frac{2 c}{a+b-c}\)
  3. C \(\frac{2 c^2}{a^2+b^2+c^2}\)
  4. D \(\frac{c}{a+b+c}\)
Verified Solution

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)}}…