3sin^2x+-2sin^2y=2sinx sin^2x+-sin^2y=?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/08/28 16:03:21

3sin^2x±2sin^2y=2sinx
sin^2x±sin^2y = (3sin^2x±2sin^2y-sin^2x)/2
= (2sinx-sin^2x)/2
= { 1 - (sinx-1)^2 }/2
-1≤sinx≤1
-2≤sinx-1≤0
0≤(sinx-1)^2≤4
-4≤-(sinx-1)^2≤0
-3≤ 1 - (sinx-1)^2 ≤ 1
-3/2 ≤ {1 - (sinx-1)^2 }/2 ≤ 1/2
即：sin^2x±sin^2y∈【-3/2,1/2】

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