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]