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CDS 2022 · PYQ · Trigonometry · medium

If cosθ + secθ - 2 = 0, where 0 ≤ θ < π/2, then what is the value of cos⁴θ + sec⁴θ - 2?

Answer

The correct answer is D: 0. cosθ + secθ = 2 implies cosθ = 1 (since AM≥GM and equality when cosθ=secθ=1). Then cos⁴θ + sec⁴θ - 2 = 1+1-2 = 0.

  1. A.-2
  2. B.2
  3. C.-1
  4. D.0✓ Correct

Explanation

cosθ + secθ = 2 implies cosθ = 1 (since AM≥GM and equality when cosθ=secθ=1). Then cos⁴θ + sec⁴θ - 2 = 1+1-2 = 0.
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