Why does Cassius profess friendship to Brutus in The Tragedy of Julius Caesar? What sort of person is Cassius?
Cassius knows that Brutus is an honorable man, and someone that the people of Rome would believe to be so as well. It is no secret that Cassius is not a fan of Caesar, and he even admits this to Brutus early on, citing such instances as Caesar not being able to swim across the river without crying for help, while he himself had no problems whatsoever.
This being said, Cassius knows that any attempt on his part to publically incite anger against Caesar would be seen as nothing more than a personal vendeta with little to no political value. The city isn't going to rise up against the most powerful man in the empire without a good deal of proof as to why it's necessary.
This is where Brutus comes into play. If Cassius can convince Brutus to join the cause, his conspiracy will gain instant credibility. Other political players will join with less reservation if they see a powerful figure such as Brutus on Cassius' side. While he is not an honorable person, and admittedly has flaws, Cassius is definitely not lacking in his cunning and intellect.
Finally, convincing Brutus that he is a friend solidifies the pact between the two. Brutus is initially against the idea of a secret pact, noting that such agreements are generally needed only for dark or illnoble deeds. The bond of friendship, however, goes much deeper than an agreement based upon mutual goals; even when things turn sour, friendship will remain.
He does this so that Brutus joins the conspiracy to kill Caesar. He knows that Brutus is a respectable man and that the people of Rome like him and if he were to join them, the people would not react with violence and want to kill them. He eventually convinced him to join them.