求sin2x+cos2x的单调区间

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因为根据公式asinx+bcosx=根号a^2+b^2sin(x+θ） ∴sin2x+cos2x=根号2sin(2x+π/4) ∴-π/2+2kπ≤2x+π/4≤π/2+2kπ k∈z ∴-3π/8+kπ≤x≤π/8+kπ k∈z π/2+2kπ≤2x+π/4≤3π/2+2kπ k∈z ∴π/8+kπ≤x≤5π/8+kπ k∈z ∴单调增区间为[-3π/8+kπ,π/8+kπ] k∈z 单调减区间为[π/8+kπ,5π/8+kπ] k∈z