Question

Решить уравнение
1-tg^2 x=2tgx

Answer 1

$1-tg^2x=2tgx$
$tg^2x+2tgx-1=0$
$left[begin{array}{ccc}tgx=-1- sqrt{2} \tgx=-1+ sqrt{2} \end{array}[tex] left[begin{array}{ccc}x=-arctg(1+ sqrt{2} )+pi*n\x=arctg( sqrt{2} -1)+pi*n\end{array}$] [/tex]
Ответ: x=-arctg(√2+1)+πn; x=arctg(√2-1)+πn, n∈Z