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NDA 1 2025 Maths, question 42

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.

Q42

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

  1. (a) sec⁡4α\sec 4\alpha
  2. (b) csc⁡4α\csc 4\alpha
  3. (c) 2sec⁡4α2\sec 4\alpha
  4. (d) 2csc⁡4α2\csc 4\alphaCorrect answer

Solution.

Answer: (d) 2csc⁡4α2\csc 4\alpha

  1. Use cot⁡t−tan⁡t=2cot⁡2t\cot t - \tan t = 2\cot 2t.
  2. Then p+q=2cot⁡2α−2cot⁡4αp + q = 2\cot 2\alpha - 2\cot 4\alpha.
  3. Since cot⁡t−cot⁡2t=csc⁡2t\cot t - \cot 2t = \csc 2t, the sum is 2csc⁡4α2\csc 4\alpha.