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In this paper we consider the coverage problem for target detection applications in wireless sensor networks. Unlike conventional coverage problems which assume sensing regions are disks around sensors, we define the sensing region according to detection constraints in terms of false alarm probability and missing probability. We show that exploiting cooperation between sensors can extend the overall sensing region while maintain the same constraints on false alarm probability and missing probability. We then propose an energy efficient cooperative detection scheme and study the trade-offs on energy consumption between cooperative and non-cooperative schemes. The cooperative scheme can use half the number of sensors to monitor the whole field compared to disk model in networks deployed on grids. We also study the communication overheads incurred by the cooperative scheme, and show that only cooperation between limited number of nearby sensors is profitable in terms of energy consumption. In our simulations on randomly deployed networks, cooperation reduces the number of sensors to cover the area by 30% and nearly doubles the number of disjoint sensor sets where each can fully cover the area. Appropriately trading off energy consumption with coverage extension, our cooperative detection scheme can increase the network lifetime by nearly 70%.