Answer:

About these authors, the answer depends on the author.

In the case of Cornelius Tacitus, as far as I know, there is no significant evidence that any of the writings attributed to him are forgeries.  I am not sure how or where you might have heard this charge, but I believe you can say with confidence that this is simply not true and scholars will not agree with this charge.  Here is the famous statement about Jesus from Tacitus:

Not all the relief that could come from the man, not all the bounties that the prince could bestow, nor all the atonements which could be presented to the gods, availed to relieve Nero from the infamy of being believed to have ordered the conflagration, the fire of Rome.  Therefore, to squelch the rumor, Nero created scapegoats and subjected to the most refined tortures those whom the common people called ‘Christians,’ [a group] hated for their abominable crimes.  Their name comes from Christ, who, during the reign of Tiberius, had been executed by the procurator Pontius Pilate.  Suppressed for the moment, the deadly superstition broke out again, not only in Judea, the land which originated this evil, but also in the city of Rome, where all sorts of horrendous and shameful practices, from every part of the world converge and are fervently cultivated.       Annals 15.44

Like I said, as far as I know, there is no significant evidence that brings into question that the person we know as Tacitus wrote these words.

The case with Josephus is different.  Josephus was a Jewish historian who wrote about the Jews in Rome for the Emperor Domitian in about AD 94.  He did not say very much about Jesus Christ or Christians, but there is one key passage in his Antiquities of the Jews which is both important and controversial.   Josephus is generally a reliable and accurate historian, although he has a tendency to exaggerate numbers at times.  The relevant passage is known as the “Testimonium Flavium” (Antiquities 18:3.3)   There is evidence that our oldest Greek manuscript of Josephus’ Antiquities has an interpolation (which means a later addition not in the original), probably from a Christian writer.  It is quite unfortunate that this Christian person attempted to manipulate Josephus’ comments about Jesus, because it had the opposite effect of what he wanted, which was to increase belief in the biblical Jesus.  As a resutl he brought the entire quote into question.  I am including the entire quote from this Greek manuscript below.  As you read it, consider the words that are in italics.  It is these words that are most likely the interpolation.  We know this because there is an Arabic translation of Josephus that has the same quote, except without the words in italics.   I will include below a version of the Testimonium Flavium which is probably what Josephus originally wrote, because it is what is contained in the early Arabic manuscript.  It actually reads more smoothly than the interpolated version, and it also sounds much more like an unbeliever like Josephus would have written.

About this time there lived Jesus, a wise man, if indeed one ought to call him a man.  For he was one who wrought surprising feats and was a teacher of such people as accept the truth gladly.  He won over many Jews and many of the Greeks.  He was the Messiah.  When Pilate, upon hearing him accused by men of the highest standing amongst us, had condemned him to be crucified, those who had in the first place come to love him did not give up their affection for him.  On the third day he appeared to them restored to life, for the prophets of God had prophesied these and countless other marvelous things about him.  And the tribe of Christians, so called after him, has still to this day not disappeared.

Agapius, an Arab Christian in 9^th century probably quotes the original, leaving out the parts in parenthesis.  Note the passage reads grammatically well without the parts in italics.   Here is the quote without the interpolation:

About this time there lived Jesus, a wise man.  For he was one who wrought surprising feats and was a teacher of such people as accept the truth gladly.  He won over many Jews and many of the Greeks.  When Pilate, upon hearing him accused by men of the highest standing amongst us, had condemned him to be crucified, those who had in the first place come to love him did not give up their affection for him.  For the prophets of God had prophesied these and countless other marvelous things about him.  And the tribe of Christians, so called after him, has still to this day not disappeared.

My answer to your question is this.  No!  The writings of Josephus are not a forgery.  However, there has almost certainly been an interpolation into his text by a later Christian writer.  There is little doubt that Josephus wrote the passage in the shorter version included above, although it is not possible to prove this beyond a doubt, as is the case with all ancient documents.

John Oakes