Undercover F.B.I operations, once seen as a last resort, are now used in about two of every three prosecutions involving people suspected of supporting the Islamic State, The increase in the number of these secret operations, which put operatives in the middle of purported plots, has come with little public or congressional scrutiny, and the stings rely on F.B.I. guidelines that predate the rise of the Islamic State. These 'stings' in terrorism cases, employsagents and informants to pose as jihadists, bomb makers, gun dealers or online “friends” in hundreds of investigations into Americans suspected of supporting the Islamic State, records and interviews show.