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

1个回答

  • 2sin^2x+sin^2y=3sinx

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

    sin^2x+sin^2y

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

    =-sin^2x+3sinx

    =-(sin^2x-3sinx+9/4)+9/4

    =-(sinx-3/2)^2+9/4

    最大值=-(1-3/2)^2+9/4=2

    最小值=-(-1-3/2)^2+9/4=-4

    取值范围是[-4,2]

    如果本题有什么不明白可以追问,如果满意记得采纳

    如果有其他问题请另发或点击向我求助,答题不易,请谅解,谢谢.

    祝学习进步!