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NDA 2 2024 Maths, question 26

Topic: Trigonometry

Q26Not scored: no correct option as printed

What is the number of solutions of the equation cot⁡2x⋅cot⁡3x=1\cot 2x\cdot \cot 3x=1 for 0<x<π0<x<\pi?

  1. (a) Only one
  2. (b) Only two
  3. (c) Only five
  4. (d) More than five

Solution.

Not scored: no correct option as printed.

Answer: not scored. No option is correct as printed.

  1. Where both cotangents exist, the equation is cos2x cos3x=sin2x sin3x, or cos5x=0.
  2. Candidates in (0,π) are π/10,3π/10,π/2,7π/10,9π/10.
  3. Exclude π/2 because sin2x=0 makes cot2x undefined.
  4. The remaining four satisfy the original equation.
  5. None of the supplied options says four; counting all five would retain an undefined point.