Question

tgx <0; ctgx>0; cosx<0;

Answer 1

$tgx textless 0; xin (frac{pi}{2}+pi n;pi +pi n); ,; nin Z\\ctgx textgreater 0; ,; xin (pi n;frac{pi}{2}+pi n); ,; nin Z\\cosx textgreater 0; ,; xin (-frac{pi}{2}+2pi n;frac{pi}{2}+2pi n); ,; nin Z$

$cosx textless 0,xin (frac{pi}{2}+2pi n;frac{3pi}{2}+2pi n),nin Z$