How can you use chromatography to find out if an unknown pure liquid is 1-pentene, cis-2-pentene or trans-2-pentene?
In order to solve the problem as stated, identify the pentenes by chromatography, you need to demonstrate a separation of the three candidates. The most likely and simplest method would be gas chromatography. If you can separate them, then you could compare the retention time of your unknown with that of each of the known pentenes. You could further verify the identity by mixing the unknown with the suspected pentene and demonstrate that it gives a single peak.
Because these pentenes are known and the problem states the unknown is a pure liquid, if IR were an acceptable method, then simply taking an IR and comparison with an authentic sample could verify with pentene were present. In making a comparison, one must compare the fingerprint region, "peak for peak".