After the match Trundle and Tate were pictured brandishing a flag with an offensive anto-Cardiff comment on, Swansea and Bluebirds fans have a long history of violent clashes. Trundle also wore a T-Shirt with a similar comment on.
South Wales Police chief superintendent Bob Evans told PA Sport: "We've had a number of complaints – many from Swansea fans it must be said – and are therefore obliged to launch a full investigation into the matter.
"We take a very dim of this matter because there were a lot of families and young children at the game and it is noticeable that many Swansea fans have themselves come to us to make a complaint - it has not been only Cardiff fans.
"I want this matter cleared up as quickly as possible because Swansea could be playing in Cardiff again in a few weeks' time if they get to the League One play-off final."