已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是

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已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是已知3sin^2x+2s

已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是
已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是

已知3sin^2x+2sin^2y=2sinx,则sin^2x+xin^2y的取值范围是
3sin^2x+2sin^2y=2sinx
∴ 2sin²y=2sinx-3sin²x≥0
∴ 0≤sinx≤2/3
∴2*( sin^2x+xin^2y)
=2sin²x+2sinx-3sin²x
=-sin²x+2sinx
=-(sinx-1)²+1
∴ sinx=0时,2*( sin^2x+xin^2y)有最小值0,即sin^2x+xin^2y的最小值为0
sinx=2/3时,2*( sin^2x+xin^2y)有最大值8/9,即sin^2x+xin^2y的最小值为4/3
∴ sin^2x+xin^2y的取值范围是【0,4/3】