Part of Prospero's "project" is to bring Miranda and Ferdinand together. At this point is Prospero's anger genuine or feigned? Explain why?
Since you talk about Prospero's plan to bring Miranda and Ferdinand together, I assume you are talking about the part late in Act I Scene 2 where Prospero is acting as if he does not trust Ferdinand. He accuses Ferdinand of coming to the island to steal it from Prospero. This is the part where Prospero says
One word more. I charge thee
That thou attend me. Thou dost here usurp
The name thou owest not, and hast put thyselfUpon this island as a spy to win it From me, the lord on ’t.
I do not think that Prospero is truly angry here. He has already shown us by this point in the scene that he really wants Miranda and Ferdinand to fall in love with one another. So he surely is not really mad at Ferdinand -- he just wants Ferdinand not to feel too confident and he wants Ferdinand to feel he still has to prove himself to Miranda's father.
In order to answer your question, I need you to be a bit more specific! At what specific point in the play are you referring to in this question?