Question

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

Answer 1

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