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NDA 1 2024 Maths, question 40

Topic: Trigonometry

Q40

What is the number of solutions of (sin⁡θ−cos⁡θ)2=2(\sin \theta-\cos \theta)^{2}=2 where −π<θ<π-\pi<\theta<\pi ?

  1. (a) Only one
  2. (b) Only twoCorrect answer
  3. (c) Four
  4. (d) No solution

Solution.

Answer: (b) Only two

  1. The condition gives 1 − sin 2θ = 2, hence sin 2θ = −1 and θ = −π/4 + kπ.
  2. Exactly two values, −π/4 and 3π/4, lie in −π < θ < π.
  3. Thus the number of solutions is two.