做变换
y = sinx [ 1/cosx - sinx/tanx + sinx ]
= sinx [ 1/cosx - cosx + sinx ]
= sinx [ (1-cos^2x)/cosx + sinx ]
= sinx [ sin^2x/cosx + sinx ]
可见,在π/6≤x≤π/3范围,y(x) 的值随x增大而增大,即
最大值为 y(π/3) = 3(1+√3)/4
最小值为 y(π/6) = √3/3 + (1-√3)/4