2026 · Q39
If sin⁴x + cos⁴x = 1, where 0 ≤ x ≤ π/2, then what is sin x ⋅ cos x equal to?
Elementary MathematicsTrigonometry
- A0
- B1/2
- C3/4
- D1
Explanation
Use the identity sin⁴x + cos⁴x = (sin²x + cos²x)² − 2sin²xcos²x = 1 − 2sin²xcos²x. Setting this equal to 1 gives sin²xcos²x = 0. Taking square roots, sin x·cos x = 0, option A.