TS EAMCET · Maths · Properties of Triangles
In a triangle \(\mathrm{ABC},\left(r_2+r_3\right) \operatorname{cosec}^2\left(\frac{\mathrm{~A}}{2}\right)=\)
- A \(4 \mathrm{R} \cot \left(\frac{\mathrm{A}}{2}\right)\)
- B \(2 \mathrm{R} \cot ^2\left(\frac{\mathrm{~A}}{2}\right)\)
- C \(\frac{4 \mathrm{R}}{\tan ^2\left(\frac{\mathrm{~A}}{2}\right)}\)
- D \(\frac{2 \mathrm{R}}{\tan \left(\frac{\mathrm{A}}{2}\right)}\)
Answer & Solution
Correct Answer
(C) \(\frac{4 \mathrm{R}}{\tan ^2\left(\frac{\mathrm{~A}}{2}\right)}\)
Step-by-step Solution
Detailed explanation
\(r_2+r_3 = 4R \cos\left(\frac{\mathrm{A}}{2}\right) \sin\left(\frac{\mathrm{B}+\mathrm{C}}{2}\right)\) \(r_2+r_3 = 4R \cos\left(\frac{\mathrm{A}}{2}\right) \sin\left(\frac{\pi-\mathrm{A}}{2}\right)\)…
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