How to sync my iphone without losing my music?

Long story short i had to do system recovery on my pc
but i neglected to backup itunes
and all the music is gone
is there anyway to sync without losing my data

No, there's no way you can get your music back. I've had that before, but it's one iTunes library per computer, and if your library is completely gone without any backup, then you lost your data.

One suggestion: There are programs called music extracters. They extract the music files already from your iPhone, and insert them into iTunes. All you have to do when you extracted the music, is just re-make your playlists. Google them. If you had a iTunes account, and if you bought music, then all the music files will be still on your iTunes account. Just view the "Purchased" tab, and you can sync it back. Hope this helps.

Yes. I have done this recently.
1.Re-install iTunes
2. Go to store in toolbar and click authorize pc
3. Transfer all purchases (I think it's in either file or edit)
And that should do it. If you have a music downloader go to your iPod click apps and go down to the music downloader. And save all on there to a separate file. Make it clear that it has music in it. Then after restoring the iPod I believe you have to go back to your iPod click on apps again and select all apps to restore. This takes a while but it works. After you select them all to restore hit sync and there you go