函数y=(2 sinx)/(2-sinx)的最大值为
问题描述：
函数y=(2 sinx)/(2-sinx)的最大值为
答
y = (2+sinx)/(2-sinx)
2y-ysinx = 2+sinx
2y-2 = sinx+ysinx = (1+y)sinx
sinx = 2(y-1)/(y+1)
-1 ≤ sinx ≤ 1
-1 ≤ 2(y-1)/(y+1) ≤ 1
1/3 ≤ y ≤ 3
∴值域是y∈[1/3,3]