Ctg(pi/2-arctg(-2017))

[latex]ctg( frac{ pi }{2}+arctg2017)= frac{cos( frac{ pi }{2}+arctg2017)}{sin( frac{ pi }{2}+arctg2017 )}= \frac{cos frac{ pi }{2}cos(arctg2017)-sin frac{ pi }{2}sin(arctg2017)}{sin frac{pi}{2}cos(arctg2017)+cos frac{pi}{2}sin(arctg2017)}= frac{-sin(arctg2017)}{cos(arctg2017)}=\-tg(arctg2017)=-2017[/latex]