AP EAMCET · Maths · Properties of Triangles
If the sides \(a, b, c\) of the triangle \(A B C\) are in harmonic progression, then \(\operatorname{cosec}^2 \mathrm{~A} / 2, \operatorname{cosec}^2 \mathrm{~B} / 2, \operatorname{cosec}^2 \mathrm{C} / 2\) are in
- A Arithmetico-geometric progression
- B Arithmetic progression
- C Geometric progression
- D Harmonic progression
Answer & Solution
Correct Answer
(B) Arithmetic progression
Step-by-step Solution
Detailed explanation
Given \(a, b, c\) are in HP, so \(1/a, 1/b, 1/c\) are in AP. Thus, \(2/b = 1/a + 1/c\), which implies \(2ac = b(a+c)\). Using the half-angle formula for cosec square: \(\operatorname{cosec}^2 A/2 = \frac{bc}{(s-b)(s-c)}\) \(\operatorname{cosec}^2 B/2 = \frac{ac}{(s-a)(s-c)}\)…
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