AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C, \frac{a}{\tan A}+\frac{b}{\tan B}+\frac{c}{\tan C}\) is equal to
- A \(2r\)
- B \(r +2R\)
- C \(2r + R\)
- D \(2(r+R)\)
Answer & Solution
Correct Answer
(D) \(2(r+R)\)
Step-by-step Solution
Detailed explanation
\( \frac{a}{\tan A} = \frac{2R \sin A}{\sin A / \cos A} = 2R \cos A \) \( \frac{a}{\tan A} + \frac{b}{\tan B} + \frac{c}{\tan C} = 2R \cos A + 2R \cos B + 2R \cos C \) \( = 2R (\cos A + \cos B + \cos C) \) \( = 2R (1 + 4 \sin(A/2) \sin(B/2) \sin(C/2)) \) \( = 2R (1 + r/R) \)…
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