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JEE Mathematics · Hard

Trigonometry: Cot identity MCQ

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Cot identityHardQuestion 200047

Question

In a triangle, cot(A/2) + cot(B/2) + cot(C/2) equals:
  1. A
    4R/r
  2. B
    s/r
    Correct
  3. C
    Δ/(rs)
  4. D
    r/s

Correct answer

s/r

Explanation

This is a standard triangle result: cot(A/2) + cot(B/2) + cot(C/2) = s/r, where s = semi-perimeter and r = inradius.

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