\(TP[f_, c_, {a_, b_}, n_Integer] := 
      \((g = Normal[Series[f, {x, c, n}]]; 
	
        Plot[{f, g}, {x, a, b}, PlotLabel -> n, 
          PlotStyle
             -> {{AbsoluteThickness[2], RGBColor[0, 0, 1]}, {
                AbsoluteThickness[2], RGBColor[1, 0, 0]}}]; Clear[g])\)\)

\(TPP[f_, c_, {a_, b_}, n_Integer] := 
      \((g = Normal[Series[f, {x, c, n}]]; Print[g]; 
	
        Plot[{f, g}, {x, a, b}, PlotLabel -> n, 
          PlotStyle
             -> {{AbsoluteThickness[2], RGBColor[0, 0, 1]}, {
                AbsoluteThickness[2], RGBColor[1, 0, 0]}}]; Clear[g])\)\)

TP[Cos[x], 0, {-15, 15}, 2]

Do[TP[ArcTan[x], 0, {-1.1, 1.1}, k], {k, 0, 80, 5}]