Найти tg^2a+ctg^2a, если tg(a)+ctg(a) = 9

т.к. tg(a)*ctg(a) = 1, тогда [latex] tg^2(a) + ctg^2(a) = tg^2(a) + 2 + ctg^2(a) - 2 = tg^2(a) + [/latex] [latex] + 2 \cdot tg(a)\cdot ctg(a) + ctg^2(a) - 2 = [/latex] [latex] = ( tg(a)+ctg(a) )^2 - 2 = 9^2 - 2 = 81-2 = 79 [/latex]