Question

Tg^3x + tg^2x - tgx - 1 > 0 решите неравенство

Answer 1

$tg^3x+tg^2x-tgx-1\ \textgreater \ 0 \; ,\; \; \; ODZ:\; \; x\ne \frac{\pi}{2}+\pi n,\; n\in Z \\\\tg^2x(tgx+1)-(tgx+1)\ \textgreater \ 0\\\\(tgx+1)(tg^2x-1)\ \textgreater \ 0\\\\(tgx-1)(tgx+1)^2\ \textgreater \ 0\\\\Tak\; kak\; (tgx+1)^2\ \textgreater \ 0\; ,\; \; to\; \; tgx-1\ \textgreater \ 0\\\\tgx\ \textgreater \ 1\\\\\frac{\pi}{4}+\pi n\ \textless \ x\ \textless \ \frac{\pi}{2}+\pi n,\; n\in Z$