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NDA 2016 Maths · Mathematics · Properties of Triangles · hard

In a triangle ABC, cot Acot B=2 and cot Bcot C=3. Then cot Ccot A is equal to

Single correct option

In a triangle ABCABC, cot⁡Acot⁡B=2\cot A\cot B=2 and cot⁡Bcot⁡C=3\cot B\cot C=3. Then cot⁡Ccot⁡A\cot C\cot A is equal to
  1. A. 44
  2. B. −4-4
  3. C. 11
  4. D. −6-6
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Answer: (B) −4-4

For a triangle A+B+C=πA+B+C=\pi, so cot⁡Acot⁡B+cot⁡Bcot⁡C+cot⁡Ccot⁡A=1\cot A\cot B+\cot B\cot C+\cot C\cot A=1. Substituting, 2+3+cot⁡Ccot⁡A=12+3+\cot C\cot A=1 gives cot⁡Ccot⁡A=−4\cot C\cot A=-4. The negative value means one angle is obtuse. Multiplying the two given values (6) is not meaningful here.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake