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The underlay cognitive radio-based hybrid radio frequency/free-space optical (RF/FSO) systems have emerged as a promising technology due to their ability to eliminate spectrum scarcity and spectrum under-utilization problems. The physical layer security of such a network with a primary user, a secondary source, a secondary receiver, and an eavesdropper is therefore examined in this work. In this network, secret communication occurs between two reliable secondary peers over the RF and FSO links simultaneously, and the eavesdropper can only overhear the RF link. In particular, the maximum transmits power limitation at the secondary user as well as the permissible interference power restriction at the primary user are also taken into consideration. All the RF and FSO links are modeled with $\alpha$-$\mu$ fading and Málaga turbulence with link blockage and pointing error impairments. At the receiver, the selection combining diversity technique is utilized to select the signal with the best electrical signal-to-ratio (SNR). Furthermore, to examine the secrecy performance taking into account the effects of each system parameter, closed-form expressions for the secrecy outage probability and effective secrecy throughput are derived. The resultant expressions are finally verified by Monte-Carlo simulations.