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α∈(0,π/2) α+π/4∈(π/4,3π/4) sinα+cosα =√2(√2/2*sinα+√2/2*cosα) =√2(sinαcosπ/4+cosαsinπ/4) =√2sin(α+π/4) sin(α+π/4)∈[√2/2,√2] 即sinα+cosα∈[√2/2,√2] 因為√2
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