已知sinx-siny=1/3 求z=cos^2y+2sinx的最大值和最小值

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已知sinx-siny=1/3 求z=cos^2y+2sinx的最大值和最小值

sinx-siny=1/3,sinx=siny+1/3
(cosy)^2+(siny)^2=1,(cosy)^2=1-(siny)^2
z=cos^2y+2sinx
z=1-(siny)^2+2(siny+1/3)
z=-(siny)^2+2siny+5/3
z=-(siny-1)^2+2/3
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