How do cockroaches become resistant to sprays spread on them after some period of time

This is an example of natural selection. There were some cockroach in the population that were resistant to the pesticide; however, they were very low in number. The resistance may be developed due to the variations in genes during reproduction or by mutations. When the pesticide was sprayed for several period of time, the resistant cockroach grow in number as they were better adapted and had higher rate of survival. After several generation, there would be only the resistant cockroach and all the cockroach that were sensitive to the pesticide spray would be eliminated from the population.