[tex]\displaystyle\bf\\\frac{Sin2\alpha +Sin6\alpha }{Cos2\alpha +Cos6\alpha } =\frac{2Sin\dfrac{2\alpha +6\alpha }{2} Cos\dfrac{2\alpha -6\alpha }{2} }{2Cos\dfrac{2\alpha +6\alpha }{2} Cos\dfrac{2\alpha -6\alpha }{2} } =\\\\\\=\frac{Sin4\alpha Cos2\alpha }{Cos4\alpha Cos2\alpha } =\frac{Sin4\alpha }{Cos4\alpha } =tg4\alpha[/tex]