Question

Найдите: $tg^{2}alpha+ctg^{2}alpha$

Если: $tgalpha+ctgalpha=2$

Answer 1

$(tg alpha +ctg alpha )^2=tg^2 alpha +ctg^2 alpha +2tg alpha cdot ctg alpha =tg^2 alpha +ctg^2 alpha +2\\2^2=tg^2 alpha +ctg^2 alpha +2\\tg^2 alpha +ctg^2 alpha =4-2=2$