Describe the motif of disguise in the texts of Sir Gawain and the Green Knight and Hamlet.

A motif in literature is an idea or theme that recurs throughout the text. In both Hamlet and Sir Gawain and the Green Knight, key characters use disguise—or more accurately, deception—to achieve their ends.
In Sir Gawain and the Green Knight, it is the Green Knight himself, Bertilak, who is quite literally disguised, both at the beginning of the story when he arrives at King Arthur's court to issue his challenge and a year later when he challenges Gawain again. (A secondary level of deception comes from the fact that Bertilak's disguise is crafted by the sorceress Morgan Le Faye, herself in disguise as an old woman at the time.)
Bertilak's intentions at first appear to be bad: when he reveals himself as Bertilak, the audience knows that Gawain has failed to keep his promise completely. He had promised Bertilak, the nobleman, to render back to him any gift he had received. Instead, cowardice causes Gawain to keep quiet about the green girdle he receives from Bertilak's wife, having been told it would save him from the Green Knight's blow. Ultimately, however, Bertilak's disguise serves a different purpose. He knows Gawain has the green girdle and that it indicates he is not as pure a knight as others believe, but he spares Gawain as a way of teaching him a lesson. Gawain will wear the girdle ever after as a reminder of this failing in his courage.
In Hamlet, disguise and deception also appear but for the most part in the figure of Hamlet himself. Hamlet at least partially feigns madness to convince Polonius and Claudius he is not stable enough to be plotting revenge against them. His use of deception serves his own purposes, and indeed Polonius suspects that his madness has "method in't." In response to this, we could also argue for the deception motif appearing again when Polonius conceals himself in order to listen in on Hamlet's conversation with his mother, following his hunch to try and discern what Hamlet is up to.
So, in Hamlet the deception helps the characters serve their own purposes, whereas in Sir Gawain and the Green Knight we could argue that Bertilak, while entertaining himself, is also furthering Gawain's chivalric education by teaching him a lesson.