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CDS 2025 · PYQ · Trigonometry · easy

If sin α + cos α = √2, where 0 < α < π/2, then what is sin³α − cos³α equal to?

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

Explanation

sin α + cos α = √2 means α = π/4 (since maximum of sin + cos is √2 at α = π/4). Then sin α = cos α = 1/√2, so sin³α − cos³α = 0.
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