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Cognitive radio is a desirable technique for secondary users to utilize the spectrum gray space. In order to avoid intolerable interference to primary users, the transmission power of cognitive radios must be carefully managed. In this paper, we analyze the sum transmission power of a group of randomly distributed but fully cooperated secondary transmitters in a network consisting of one primary transmitter and multiple randomly distributed primary receivers. The sum power is given by numerical integrations, or by closed-form approximate expressions. The results indicate that significant secondary transmission power is allowable, depending on the distance of primary and secondary transmitters, as well as the numbers of primary receivers and secondary transmitters. Such results are verified in simulations.