Question

Determinati numarul real x, stiind ca tgx+ctgx+2=0??

Answer 1

Stim ca ctgx=1/tgx
tgx+(1/tgx)+2=0 => tg^2(x)+2tgx+1=0
Notam tgx=t
t^2+2t+1=0
D=4-4*1*1=0
t1=-2/2=-1
tgx=-1 => x€{arctg(-1)+k*pi} => x€{-pi/4+k*pi}, k€Z.