In this letter, a double threshold-based log-likelihood ratio (LLR) detector with a novel hard-soft combining rule (DT-LLR-HSC) is proposed for spectrum sensing in cooperative cognitive radio networks (CRNs) under the block Rayleigh fading scenario. A novel weighted hard-soft combining scheme is adopted at the fusion center to combine local binary/energy information resulting in global binary decision. A trust-based novel weight vector estimation considering both the sensing and reporting channel signal-to-noise ratio is also proposed. Further, the proposed DT-LLR-HSC scheme is adopted in full-duplex cooperative CRNs under Nakagami-m fading channel. The analytical expressions for the average probability of detection are derived and verified for both the half-duplex and full-duplex cases.