[latex] frac{sinx-sin3x}{cosx-cos3x} =-ctg2x[/latex][latex]sinx-sin3x=2*sin frac{x-3x}{2}*cos frac{x+3x}{2} =2*sin(-x)*cos2x=[/latex]=-2sinx*cos2x[latex]cosx-cos3x=-2*sin frac{x-3x}{2}*sin frac{x+3x}{2} =-2*sin(-x)*sin2x= [/latex]=2*sinx*sin2x[latex] frac{sinx-sin3x}{cosx-cos3x} = frac{-2sinx*cos2x}{2sinx*sin2x} =-ctg2x[/latex]-ctg2x=-ctg2xч.т.д.