Reliable and agile spectrum sensing as well as secure communication are key requirements of a cognitive radio system. In this paper, secrecy throughput of a cognitive radio is maximized in order to determine the sensing threshold, the sensing time, and the transmission power. Constraints of the problem are defined as a lower-bound on the detection probability, an upper-bound on the average energy consumption per time-frame, and the maximum transmission power of the cognitive radio. We show that the problem can be solved by an on-off strategy where the cognitive radio only performs sensing and transmits data if the cognitive channel gain is greater than the average eavesdropper channel gain. The problem is then solved by a line-search over sensing time. Eventually, the secrecy throughput of the cognitive radio is evaluated employing the IEEE 802.15.4/Zig-Bee standard.