Решите уравнение tg2x+tg4x=tg5x+tgx

tg2x+tg4x=tg5x+tgxsin6x/cos2xcos4x=sin6x/cos5xcosxcos2xcos4x=cos5xcosx1/2(cos2x+cos6x)=1/2(cos4x+cos6x)cos2x+cos6x=cos4x+cos6xcos2x=cos4x2cos²2x-1-cos2x=0cos2x=a2a²-a-1=0D=1+8=9a1=(1-3)/4=-1/2⇒cos2x=-1/2⇒2x=+2π/3+2πn,n∈Z⇒x=+π/3+πn,n∈Za2=(1+3)/4=1⇒cos2x=1⇒2x=2πk,k∈Z⇒x=πk,k∈Z