Question

tgx+6ctg-5=0

помогите плиз

 

 

 

 

Answer 1

$tgx+6ctgx-5=0 \ frac{1}{ctgx} +6ctgx-5=0 | *ctgx \ 1+6 ctg^{2} x-5ctgx=0 \ ctgx=t, t>0 \ 6 t^{2} -5t+1=0 \ D=5*5-4*6=25-24=1 \ t_{1} = frac{5+1}{12} = frac{6}{12} = frac{1}{2} \ t_{2} = frac{5-1}{12} = frac{4}{12} = frac{1}{3} \ ctgx= frac{1}{2} \ x_{1} =arcctg frac{1}{2}+pi n, n E z \ ctgx= frac{1}{3} \ x_{2} =arcctg frac{1}{3}+pi n, n E z$