实数x,y满足x^2+y^2=1,则x+y+2/x-y+2的最大值和最小值分别为多少

题目

实数x,y满足x^2+y^2=1,则x+y+2/x-y+2的最大值和最小值分别为多少
应该是（x+y+2)/(x-y+2)的最大值和最小值为多少，谢谢各位大虾帮助。

答案

解；令x=sint,y=cost令Y=(x+y+2)/(x-y+2)=(sinx+cosx+2)/(sinx-cosx+2)整理有(1-Y)sint+(1+Y)cost=2(y-1)(1-Y)sint+(1+Y)cost=√[(1-Y)²+(1+Y)²]sin(t+ψ)=2(Y-1)|sin(t+ψ)|≤1则 |√[(1-Y)²+(1+Y)&...