sin^2x+cos^2y=1/2 求3sin^2x+sin^2y的最值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/11 03:29:14

sin^2x+cos^2y=1/2
∴sin^2x=1/2-cos^2y
3sin^2x+sin^2y
=3（1/2-cos^2y）+sin^2y
=1.5-3cos^2y）+sin^2y
又有sin^2y+cos^2y=1
∴cos^2y=1-sin^2y
原式=1.5-3（1-sin^2y）+sin^2y
=4sin^2y-1.5
0≤sin^2y≤1
∴最大值为2.5
最小值为-1.5

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