Question

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

Answer 1

т.к. tg(a)*ctg(a) = 1, тогда
$tg^2(a) + ctg^2(a) = tg^2(a) + 2 + ctg^2(a) - 2 = tg^2(a) +$
$+ 2 cdot tg(a)cdot ctg(a) + ctg^2(a) - 2 =$
$= ( tg(a)+ctg(a) )^2 - 2 = 9^2 - 2 = 81-2 = 79$