Question

Решите уравнение
tgx-2/2tgx+1=3

Answer 1

tgx-2/2tgx+1=3
x neq  pi/2+Κ  pi .x=arctg(-1/2)+Κ  pi .Κ∈Ζ
tgx-2=3(2tgx+1)
tgx-2=6tgx=3
tgx-6tgx=3+2
-5tgx=5
tgx=-1
x=arctg-1
x=-( pi /4)
x=-( pi /4)+k pi .Κ∈Ζ
x=3pi /4 +k pi .Κ∈Ζ .x  neq  arctg(-1/2)+k pi ,Κ∈Ζ
x=3pi /4 +k pi .Κ∈Ζ