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AP EAMCET · Maths · Properties of Triangles

In \(\triangle \mathrm{ABC},\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{c}{2}=\)

  1. A \(2 R \cot ^2 \frac{C}{2}\)
  2. B \(4 R \tan ^2 \frac{C}{2}\)
  3. C \(4 R \cot ^2 \frac{C}{2}\)
  4. D \(2 R \tan ^2 \frac{C}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(4 R \cot ^2 \frac{C}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {In } \triangle \mathrm{ABC}, \mathrm{~A}+\mathrm{B}+\mathrm{C}=\pi \\ & \because r_1+r_2=4 \mathrm{R} \sin \frac{\mathrm{~A}}{2} \cdot \cos \frac{\mathrm{~B}}{2} \cdot \cos \frac{\mathrm{C}}{2}+4 \mathrm{R} \cos \frac{\mathrm{~A}}{2} \cdot \sin…