2025 · Q31
If sin α + cos α = √2, where 0 < α < (π)/(2), then what is sin³ α - cos³ α equal to?
Elementary MathematicsTrigonometry
- A1
- B1/2
- C1/4
- D0
Explanation
Squaring sinα + cosα = √2 gives 1 + sin 2α = 2, so sin 2α = 1 and 2α = π/2 (α ∈ (0, π/2)), i.e. α = π/4. Then sin³α − cos³α = (√2/2)³ − (√2/2)³ = 0, option (d).