Sycophancy refers to the tendency of a large language model to align its outputs with the user's perceived preferences, beliefs, or opinions, in order to look favorable, regardless of whether those statements are factually correct. This behavior can lead to undesirable consequences, such as reinforcing discriminatory biases or amplifying misinformation. Given that sycophancy is often linked to human feedback training mechanisms, this study explores whether sycophantic tendencies negatively impact user trust in large language models or, conversely, whether users consider such behavior as favorable. To investigate this, we instructed one group of participants to answer ground-truth questions with the assistance of a GPT specifically designed to provide sycophantic responses, while another group used the standard version of ChatGPT. Initially, participants were required to use the language model, after which they were given the option to continue using it if they found it trustworthy and useful. Trust was measured through both demonstrated actions and self-reported perceptions. The findings consistently show that participants exposed to sycophantic behavior reported and exhibited lower levels of trust compared to those who interacted with the standard version of the model, despite the opportunity to verify the accuracy of the model's output.