Решите уравнение tg2x+tg4x=tg5x+tgx

Tg2x+tg4x=tg5x+tgx
sin6x/cos2xcos4x=sin6x/cos5xcosx
cos2xcos4x=cos5xcosx
1/2(cos2x+cos6x)=1/2(cos4x+cos6x)
cos2x+cos6x=cos4x+cos6x
cos2x=cos4x
2cos²2x-1-cos2x=0
cos2x=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒cos2x=-1/2⇒2x=+2π/3+2πn,n∈Z⇒x=+π/3+πn,n∈Z
a2=(1+3)/4=1⇒cos2x=1⇒2x=2πk,k∈Z⇒x=πk,k∈Z