Решите уравнение tgx-2/2tgx+1=3

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