This research focuses on improving cognitive radio (CR) systems, which are designed to better use the Radio Frequency (RF) spectrum. The RF spectrum is often underutilized, and CR systems aim to address this inefficiency by dynamically accessing available frequency bands. Two sensing methods are examined for their effectiveness in terms of detection accuracy and false alarm rates: Double Threshold Energy Detection and Three Event Energy Detection (3EED) with an adaptive decision threshold. A new objective function is introduced to prioritize Primary User (PU) activity over Secondary User (SU) access by incorporating weighted factors. The hybrid approach, which combines 3EED and adaptive double threshold methods, achieves superior results with minimal error and enhanced probability of detection. These insights advance the development of efficient spectrum sensing frameworks, optimizing spectrum usage in CR systems.