Question 953101
{{{cot^2(x)(1+tan^2(x))}}} ............since {{{cot^2(x)=cos^2(x)/sin^2(x)}}} and  {{{tan^2(x)=sin^2(x)/cos^2(x)}}}, we have


={{{(cos^2(x)/sin^2(x))(1+sin^2(x)/cos^2(x))}}}


={{{(cos^2(x)/sin^2(x))+(sin^2(x)/cos^2(x))(cos^2(x)/sin^2(x))}}}


={{{(cos^2(x)/sin^2(x))+(cross(sin^2(x))1/cross(cos^2(x))1)(cross(cos^2(x))1/cross(sin^2(x))1)}}}


={{{cos^2(x)/sin^2(x)+1}}}


={{{cos^2(x)/sin^2(x)+1*sin^2(x)/sin^2(x)}}}


={{{(cos^2(x)+sin^2(x))/sin^2(x)}}}


={{{1/sin^2(x)}}}

={{{sin^-2(x)}}} -> in terms of sine

or, we can use identity {{{1/sin^2(x)=csc^2(x)}}}


={{{csc^2(x)}}}