若实数x,y满足x^2+y^2=1,2xy/(x+y-1)>=m恒成立,求m范围.用三角函数怎样解?

问题描述:

若实数x,y满足x^2+y^2=1,2xy/(x+y-1)>=m恒成立,求m范围.用三角函数怎样解?

由式一 令x=sint y=cost
带入式二 化简得 [(sint-cost)^2-1]/(sint+cost-1)=sint+cost+1=根号2sin(t-a)+1>=-根号2+1
所以m