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Question 200018
JEE Mathematics · Hard

Trigonometry: Inequality MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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InequalityHardQuestion 200018

Question

The minimum value of 9 sec²θ + 16 cosec²θ is:
  1. A
    25
  2. B
    49
    Correct
  3. C
    169
  4. D
    1

Correct answer

49

Explanation

Let f = 9 sec²θ + 16 cosec²θ = 9(1+tan²θ) + 16(1+cot²θ) = 25 + 9t + 16/t where t = tan²θ. By AM-GM: 9t + 16/t ≥ 2√(9×16) = 24. Minimum f = 25 + 24 = 49.

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