Use an addition or subtraction formula to simplify the expression:
tan(π2u)=cot(f(u))\displaystyle {\tan{{\left({\frac{{\pi}}{{{2}}}}-{u}\right)}}}={\cot{{\left({f{{\left({u}\right)}}}\right)}}}.
f(u)=\displaystyle {f{{\left({u}\right)}}}=   .