Question

2 tg x -3 ctgx -1=0.

Answer 1

$2 tg x -3 ctgx -1=0;2 tg x -3 *frac{1}{tgx} -1=0;2 tg^2 x -tgx-3=0;$
$2 tg^2 x -tgx-3=0;tgx=m;2m^2-m-3=0;D=24=25;$
$m=-1;tgx=-1;x=- frac{ pi }{4}+ pi n;n in Z;$
$m=1,5;tgx=1,5;x=arctg1,5+ pi n;n in Z;$