СРОЧНООО ВЫЧИСЛИТЬ arcctg(-tg50°)
Применяем 2 формулы arcctg (-x) = π - arcctg x и arctg x = π/2 - arcctg x
![arcctg(-tg50^o)= \pi -arcctg(tg50^o)= \pi -[ \frac{ \pi }{2} -arctg(tg50^o)]=\\ \\=
\frac{ \pi }{2} +arctg(tg50^o)=\frac{ \pi }{2} +50^o=\frac{ \pi }{2} +\frac{5 \pi }{18}=\frac{14 \pi }{18}=\frac{7 \pi }{9}](https://tex.z-dn.net/?f=arcctg%28-tg50%5Eo%29%3D+%5Cpi+-arcctg%28tg50%5Eo%29%3D+%5Cpi+-%5B+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+-arctg%28tg50%5Eo%29%5D%3D%5C%5C+%5C%5C%3D%0A%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2Barctg%28tg50%5Eo%29%3D%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B50%5Eo%3D%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B%5Cfrac%7B5+%5Cpi+%7D%7B18%7D%3D%5Cfrac%7B14+%5Cpi+%7D%7B18%7D%3D%5Cfrac%7B7+%5Cpi+%7D%7B9%7D "arcctg(-tg50^o)= \pi -arcctg(tg50^o)= \pi -[ \frac{ \pi }{2} -arctg(tg50^o)]=\\ \\=
\frac{ \pi }{2} +arctg(tg50^o)=\frac{ \pi }{2} +50^o=\frac{ \pi }{2} +\frac{5 \pi }{18}=\frac{14 \pi }{18}=\frac{7 \pi }{9}")
