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NDA 2 2024 Maths, question 28

Topic: Trigonometry

Q28

In a triangle ABCABC

tan⁡A+tan⁡B+tan⁡C=k\tan A+\tan B+\tan C=k

What is the value of cot⁡Acot⁡Bcot⁡C\cot A\cot B\cot C?

  1. (a) 0.5k0.5k
  2. (b) 1/k1/kCorrect answer
  3. (c) 3/k3/k
  4. (d) 1/k31/k^{3}

Solution.

Answer: (b) 1/k1/k

  1. For defined tangents in a triangle, tan A+tan B+tan C=tan A tan B tan C.
  2. Hence the product of tangents is k, and the product of cotangents is its reciprocal 1/k.