求下列函数的值域 y=sinx/(sinx+2) y=1/(sin²x+1）

sinx≤1,sinx+2恒>0,分式有意义,x可取任意实数,函数定义域为R
整理,得
(y-1)sinx=-2y
y=1时,左=0,右=-2,等式不成立,y≠1
sinx=-2y/(y-1)
-1≤sinx≤1
-1≤-2y/(y-1)≤1
2y/(y-1)+1≥0(3y-1)/(y-1)≥0y>1或y≤1/3
2y/(y-1)-1≤0(y+1)/(y-1)≤0-1≤y