Question

найдите tg^2альфа+ctg^2альфа,если tgальфа+ctg альфа =a​

Answer 1

$tg\alpha +ctg\alpha =a\\\\(tg\alpha +ctg\alpha )^2=a^2\\\\tg^2\alpha +2\cdot \underbrace {tg\alpha \cdot ctg\alpha }_{1}+tg^2\alpha=a^2\\\\tg^2\alpha +2\cdot 1+ctg^2\alpha =a^2\\\\\boxed {\; tg^2\alpha +ctg^2\alpha =a^2-2\; }$