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NDA 2 2025 Maths, question 49

Topic: Trigonometry

Q49

If 0≤x≤π20\le x\le \frac{\pi}{2}, then what is the number of values of xx satisfying the equation tan⁡x+sec⁡x=2cos⁡x\tan x+\sec x=2\cos x?

  1. (a) 00
  2. (b) 11Correct answer
  3. (c) 22
  4. (d) 33

Solution.

Answer: (b) 11

  1. The endpoint π/2 is outside the domain of tan and sec.
  2. Multiplying by cos x for the remaining interval gives sin x+1=2(1−sin²x).
  3. Thus (2sin x−1)(sin x+1)=0.
  4. Only sin x=1/2 is possible, giving x=π/6 and one solution.