{sinx}{tan{\frac{1}{x}} = (x-{\frac{x^3}{6}}-{\frac{x^5}{120}}+o(x^5}))({\frac{1}{x}}+{\frac{1}{3x^3}}+{\frac{2}{15x^5}}+o({\frac{1}{x^5}}))={\frac{x^4}{120}}+{\frac{2}{15 x^4}}-{\frac{59 x^2}{360}}+{\frac{14}{45 x^2}}+{\frac{851}{900}}