In fushigi yuugi, tamahome and taka are one person. What happened to Tamahome when Taka was introduced?

You know, good question. It was never actually explained, I don't think. If you read further into the manga or watched the OVA following the series, I believe he disappeared from the world of the book, because the other Suzaku warriors had claimed that they hadn't seen Tamahome ever since she had returned to her world following the summoning of Suzaku. However, in the same OVA (and future of the manga), it explores Taka and Miaka's relationship in the real world, then how they are both sucked into the world of the book, and Taka comes face to face with Tamahome (or a mirror image of him).