[tex]\displaystyle\bf\\\frac{Sin14\alpha -Sin10\alpha }{Cos3\alpha -Cos7\alpha }=\frac{2Sin\frac{14\alpha -10\alpha }{2}\cdot Cos\frac{14\alpha +10\alpha }{2} }{-2Sin\frac{3\alpha +7\alpha }{2}\cdot Sin\frac{3\alpha -7\alpha }{2} } =-\frac{Sin2\alpha \cdot Cos12\alpha }{Sin5\alpha \cdotSin(-2\alpha )} =\\\\\\=\frac{Sin2\alpha \cdot Cos12\alpha }{Sin5\alpha \cdot Sin2\alpha } =\frac{Cos12\alpha }{Sin5\alpha }[/tex]