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NDA 2 2025 Maths, question 47

Topic: Trigonometry

Q47

How many values of θ\theta, where −π<θ<π-\pi<\theta<\pi, satisfy both the equations cot⁡θ=−3\cot \theta=-\sqrt{3} and cosec⁡θ=−2\operatorname{cosec} \theta=-2 simultaneously?

  1. (a) 44
  2. (b) 22
  3. (c) 11Correct answer
  4. (d) None

Solution.

Answer: (c) 11

  1. cosecθ=−2 gives sinθ=−1/2.
  2. In (−π,π), candidates are −π/6 and −5π/6.
  3. Their cotangents are −√3 and +√3 respectively.
  4. Only −π/6 satisfies both equations, so there is one value.