Question

Вычислите arcctg(-tg(200))
9tg(arcctg(-2)+arcctg4) 

Answer 1

$arcctg(-tg(270^o-70^o))=arcctg(-ctg(70^o))=-arcctg(ctg(70^o))=\ \ = -70^o$



$9tg(arcctg(-2)+arcctg (4))=9tg(arcctg (frac{-2+4}{1-(-2) cdot 4}))=9tg (arcctg(frac{2}{9}))\\=9 tg(-arctg(frac{2}{9}))=-9 cdot frac{2}{9}=-2$