Question

2 tg x -3 ctgx -1=0.

Answer 1

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