•He acted very strange infront of Ophelia and it genuinely scared her, and because she loves him and knows him sos well she knows something is really wrong.
"Lord Hamlet, with his doublet all unbraced;/ No hat upon his head, his stockings foul'd,/
Ungarter'd, and down-gyved to his ankle;/Pale as his shirt; his knees knocking each other,/And with a look so piteous in purport/As if he had been loosed out of hell/To speak of horrors, he comes before me" (II.i.87-94).
•He believes that he should've killed his uncle already and that the actor shouldn't possibly have more feelings about this than him although that is what the actor's job is to do.
"A broken voice, and his whole function suiting/ With forms to his conceit? And all for nothing!/ For Hecuba!/ What's Hecuba to him or he to Hecuba,/ That he should weep for her? what would he do,/ Had he the motive and the cue for passion/ That I have? He would drown in the stage with tears/ And cleave the general war with horrid speech" (II.ii.554-561).
•He decides that adding scenes that depict his fathers death will make Claudius outwardly guilty looking instead of just acting on it and killing Claudius, which if Hamlet wasn't mad, would be able to do.
"With most miraculous organ, I'll have these players/ Play something like the muddy of my father/ Before mine uncle. I'll observe his looks;/ I'll tent him of the quick.mId he but blench,/ I know my course" (II.ii.594-98).
I believe Hamlet isn't actually crazy and he is acting because
•He told Rosencrantz and Guildenstern, who are his friends that he was just acting crazy.
"I am but mad north-north-west. When the wind is/ southerly I know a hawk for a handsaw" (II.ii.380-81).
•He also tells Horatio and Marcellus that he is just acting.
"Here, as before, never, so help you mercy,/ How strange or odd soe'er I bear myself-/ As perchance hereafter shall think meet/ To put an antic disposition on-/ That you, at