The indiscriminate proliferation of resource-constrained Internet of Things (IoT) systems in safety-critical domains, such as smart cities, healthcare, and industrial automation, require effective trust assessment processes to enable secure and reliable functioning. Existing trust models are energy-consumptive and computationally expensive, which makes them impractical for resource-constrained low-power IoT devices with limited computing capabilities and energy resources. In this paper, we explore the critical issue of energy efficiency versus trust accuracy tradeoff in IoT networks. We introduce a novel Energy-Efficient Trust Evaluation Model (EETEM) that employs dynamic behavioural analysis, adaptive thresholding, and context-aware sampling to minimize energy consumption without compromising security. The model employs a hybrid trust score combining node interaction history, energy usage profiles, and real-time behaviour information, which are dynamically derived using lightweight cryptographic computations. Simulation on a 500-node IoT network shows that EETEM improves energy saving, speeds up trust convergence, and achieves high detection accuracy against adversarial nodes such as Sybil and colluding attackers. The model achieves these benefits through its adaptive sampling feature which cuts down data transmission by 40% and its distributed architecture which prevents single-point bottlenecks. The research shows that scalable and energy-efficient trust frameworks can be used for resource-constrained IoT applications without compromising security.