求sinA/(2-cosA)的取值范围

设sinA/(2-cosA)=k
sinA=2k-kcosA
sinA+kcosA=2k
√(1+k^2)sin(A+θ)=2k
1+k^2≥4k^2
解得-√3/3≤k≤√3/3
原函数取值范围[-√3/3,√3/3]

设：t=sinA/(2-cosA)
sinA=t(2-cosA)
[t(2-cosA)]^2+cos^2A=1
(1+t^2)cos^2A-4t^2cosA+4t^2-1=0
判别式△=16t^4-4(1+t^2)(4t^2-1)=-12t^2+4≥0
t^2≤1/3
-√3/3≤t≤√3/3

|x1|≤1,|x2|≤1
|x1+x2|=4t^2/(1+t^2)≤2,t^2≤1,满足
|x1x2|=|4t^2-1|/(1+t^2)≤1
,4t^2≥1时，3t^2≤2，满足
4t^2<1时，5t^2≤2,满足

所以，sinA/(2-cosA)的取值范围：[-√3/3,√3/3]

-1《=sinA/(2-cosA)《=3

-1/根号3≤sinA/(2-cosA)≤1/根号3