[tex]\displaystyle\bf\\\frac{Sin3\alpha }{Sin\alpha } -\frac{Cos3\alpha }{Cos\alpha } =\frac{Sin3\alpha \cdot Cos\alpha -Cos3\alpha \cdot Sin\alpha }{Sin\alpha Cos\alpha } =\\\\\\=\frac{Sin(3\alpha -\alpha )}{Sin\alpha Cos\alpha } =\frac{Sin2\alpha }{Sin\alpha Cos\alpha } =\frac{2\cdot Sin2\alpha }{2\cdot Sin\alpha Cos\alpha } =\frac{2Sin2\alpha }{Sin2\alpha } =2\\\\\\2=2 \ -verno[/tex]

Тождество доказано