Question

ctgx=-4-3tgx ешите пожалуйста!!!!)))

Answer 1

$ctgx=-4-3tgx\\ ctgx+3tgx+4=0\\ \\ \frac{1}{tgx}+3tgx+4=0 \ (*tgx\neq 0)\\ \\ 1+3tg^2x+4tgx=0\\ 3tg^2x+4tgx+1=0\\ D=16-12=4\\ D^2=2^2\\ tgx_1=\frac{-4-2}{6}=-1\\\\  tgx_2=\frac{-4+2}{6}= =-\frac{1}{3} \\ \\ \left \{ {{x_1=-\frac{\pi }{4}+\pi k, k \in Z } \atop {x_2=-arctg(\frac{1}{3})+\pik, k \in Z  }} \right.$