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NDA 2 2025 Maths, question 48

Topic: Trigonometry

Q48

If x+1x=2cos⁡θx+\frac{1}{x}=2\cos \theta, then what is x3+1x3x^{3}+\frac{1}{x^{3}} equal to?

  1. (a) cos⁡3θ\cos ^{3}\theta
  2. (b) cos⁡3θ\cos 3\theta
  3. (c) 2cos⁡3θ2\cos 3\thetaCorrect answer
  4. (d) 3cos⁡3θ3\cos 3\theta

Solution.

Answer: (c) 2cos⁡3θ2\cos 3\theta

  1. Use (x+1/x)³=x³+1/x³+3(x+1/x).
  2. Hence x³+1/x³=8cos³θ−6cosθ=2cos3θ, by the triple-angle identity.