ctg (π/2-3X)=tg2x+tgx (Учтём, что ctg (π/2-3X) = tg3x)
tg3x = tg2x +tgx
Sin3x/Cos3x = Sin3x/(Cos2xCosx),
Sin3x/Cos3x - Sin3x/(Cos2xCosx) = 0,
Sin3x(1/Cos3x - 1/(Cos2xCosx) ) =0
Sin3x = 0 или 1/Cos3x - 1/(Cos2xCosx) = 0
3x = πn, n ∈Z (Cos2xCosx -Cos3x)/(Cos3xCos2xCosx)=0
x = πn/3, n ∈Z Cos2xCosx -Cos3x=0
Cos3xCos2xCosx≠0,⇒
Cos2xCosx - Cos(2x+x) =0,⇒
Cos2xCosx -Cos2xCosx -Sin2xSinx = 0,⇒
Sin2xSinx = 0,⇒
Sin2x = 0 или Sinx = 0
2x = πk , k ∈Z x = πm, m ∈Z
x = πk/2, k ∈Z