设sinx+siny=1/3,求m=sinx-cos2y(cos的平方y)的最大值和最小值.

sinx=1/3-siny 故sinx-(cosy)^2=(1/3-siny)-[1-(siny)^2] =(siny)^2-siny-2/3=(siny-1/2)^2-1/4-2/3 siny∈[-1,1],当siny=-1时,(siny-1/2)^2取得最大值为9/4,sinx-(cosy)^2取得最大值4/3.当siny=1/2时,(siny-1/2)^2...