Final answer:
Hamlet is expected to trust Rosencrantz and Guildenstern due to their past as childhood friends, but their allegiance to Claudius and role in spying on Hamlet ultimately lead to a betrayal of that trust.
Step-by-step explanation:
Hamlet could be expected to trust Rosencrantz and Guildenstern because they are his childhood friends, whom he has known for a long time. Initially, Hamlet receives them warmly, believing they are in Elsinore to visit him out of concern and friendship. However, as the play unfolds, it becomes clear that Rosencrantz and Guildenstern's loyalties lie with King Claudius, who has enlisted their help to spy on Hamlet to discover the cause of his apparent madness and later carry out his orders to have Hamlet killed in England. Despite the expectation of trust based on their shared history, Rosencrantz and Guildenstern's true intentions and allegiance to Claudius ultimately betray Hamlet's trust.