[tex]\displaystyle\bf\\\frac{Cos2\alpha -Sin2\alpha }{Cos4\alpha -Sin4\alpha +2Sin^{2} 2\alpha } =\frac{Cos2\alpha -Sin2\alpha }{1-2Sin^{2} 2\alpha -Sin4\alpha +2Sin^{2} 2\alpha } =\\\\\\=\frac{Cos2\alpha -Sin2\alpha }{1-Sin4\alpha } =\frac{Cos2\alpha -Sin2\alpha }{Cos^{2}2\alpha -2Sin2\alpha Cos2\alpha +Sin^{2} 2\alpha } =\\\\\\=\frac{Cos2\alpha -Sin2\alpha }{(Cos2\alpha -Sin2\alpha )^{2} } =\frac{1}{Cos2\alpha -Sin2\alpha }[/tex]