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NDA 1 2025 Maths, question 41

Topic: Trigonometry

Passage · Q41 to Q43

Let p=tan⁡2α−tan⁡αp = \tan 2\alpha - \tan\alpha and q=cot⁡α−cot⁡2αq = \cot\alpha - \cot 2\alpha.

Q41

What is (p/q)(p/q) equal to?

  1. (a) −tan⁡α⋅tan⁡2α- \tan\alpha \cdot \tan 2\alpha
  2. (b) −cot⁡α⋅cot⁡2α- \cot\alpha \cdot \cot 2\alpha
  3. (c) tan⁡α⋅tan⁡2α\tan\alpha \cdot \tan 2\alphaCorrect answer
  4. (d) cot⁡α⋅cot⁡2α\cot\alpha \cdot \cot 2\alpha

Solution.

Answer: (c) tan⁡α⋅tan⁡2α\tan\alpha \cdot \tan 2\alpha

  1. Write u=tan⁡αu = \tan\alpha and v=tan⁡2αv = \tan 2\alpha.
  2. Then p=v−up = v - u and q=1/u−1/v=(v−u)/(uv)q = 1/u - 1/v = (v - u)/(uv).
  3. Therefore p/q=uv=tan⁡αtan⁡2αp/q = uv = \tan\alpha\tan 2\alpha, wherever the given expressions are defined.