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NDA 2 2025 Maths, question 30

Topic: Trigonometry

Passage · Q29 to Q30

Let cos⁡(2x+3y)=12\cos (2x+3y)=\frac{1}{2} and cos⁡(3x+2y)=32\cos (3x+2y)=\frac{\sqrt{3}}{2}, where −π<(2x+3y)<π-\pi<(2x+3y)<\pi and −π<(3x+2y)<π-\pi<(3x+2y)<\pi.

Q30

How many values does (y−x)(y-x) have?

  1. (a) Two
  2. (b) Three
  3. (c) FourCorrect answer
  4. (d) More than four

Solution.

Answer: (c) Four

  1. Subtracting gives y−x=U−V.
  2. The four sign combinations of U=±π/3 and V=±π/6 yield π/6,π/2,−π/2,−π/6.
  3. All four are distinct.