sinx-cosx = √(1-sin2x) = √(sin^2x+cos^2x-2sinxcosx) = √(sinx-cosx)^2 = |sinx-cosx|
∴sinx-cosx ≥ 0
∴√2 (sinxcosπ/4-cosxsinπ/4) ≥ 0
∴√2 sin(x-π/4) ≥ 0
∴ sin(x-π/4) ≥ 0
∴x-π/4 ∈【2kπ,2kπ+π】,其中k∈Z
∴x∈【2kπ+π/4,2kπ+5π/4】,其中k∈Z