不等式sinx-cosx>1的解集是

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  • 不等式sinx-cosx>1的解集是?

    ∵sinx-cosx

    =√2[sinx×(√2/2)-cosx×(√2/2)]

    =√2[sinx×cos(π/4)-cosx×sin(π/4)]

    =√2sin[x-(π/4)]>1

    ∴sin[x-(π/4)]>√2/2

    ∴观察函数y=sinx的图像可知:

    2kπ+(π/4)