$$\eqalign{
& y = {{{{\sin }^2}x} \over {{{\cos }^2}x - \sin 2x + 1}} \cr
& \Leftrightarrow y = {{{{1 - \cos 2x} \over 2}} \over {{{1 + \cos 2x} \over 2} - \sin 2x + 1}} \cr
& \Leftrightarrow y = {{1 - \cos 2x} \over {1 + \cos 2x - 2\sin 2x + 2}} \cr
& \Leftrightarrow y + y\cos 2x - 2y\sin 2x + 2y = 1 - \cos 2x \cr
& \Leftrightarrow - 2y\sin 2x + \left( {y + 1} \right)\cos 2x = 1 - 3y \cr
& PT\,\,co\,\,nghiem \cr
& \Leftrightarrow {\left( { - 2y} \right)^2} + {\left( {y + 1} \right)^2} \ge {\left( {1 - 3y} \right)^2} \cr
& \Leftrightarrow 4{y^2} + {y^2} + 2y + 1 \ge 9{y^2} - 6y + 1 \cr
& \Leftrightarrow - 4{y^2} + 8y \ge 0 \cr
& \Leftrightarrow 0 \le y \le 2 \cr
& \Rightarrow \min y = 0;\,{\mathop{\rm maxy}\nolimits} = 2 \cr} $$
