Question 1072923
Not written well.  If you want to verify  {{{tan((1/2)x)=csc(x)-cot(x)}}}, then you eventually want to use another identity (which you can find in a reference) of {{{tan(theta/2)=(1-cos(theta))/sin(theta))}}}.


Start with the right hand side of YOUR identity to be verified.  Definitions for cosecant and cotangent give
{{{1/sin(x)-cos(x)/sin(x)}}}


{{{(1-cos(x))/sin(x)}}}


Equal by referenced identity above to 

{{{tan(x/2)}}}


DONE.