Because data dissemination is crucial to wireless sensor networks (WSNs), its energy efficiency and reliability are of paramount importance. While achieving these two goals together is highly nontrivial, the situation is exacerbated if WSN nodes are duty-cycled (DC) and their transmission power is adjustable. In this paper, we study the problem of minimizing the expected total transmission power for reliable data dissemination (multicast/broadcast) in DC-WSNs. Due to the NP-hardness of the problem, we design efficient approximation algorithms with provable performance bounds for it. To facilitate our algorithm design, we propose the novel concept of Time-Reliability-Power (TRP) space as a general data structure for designing data dissemination algorithms in WSNs, and the performance ratios of our algorithms based on the TRP space are proven to be O(log Delta log k) for both multicast and k broadcast, where Delta is the maximum node degree in the network and is the number of source/destination nodes involved in a data dissemination session. We also conduct extensive simulations to firmly demonstrate the efficiency of our algorithms.