Is it possible to use headphones to listen to music while keeping the devices battery charged?
No, there is only one mini-USB port and HTC doesn’t make a cradle expansion for the TyTN so you can either charge/sync the device or use the original headphones. Expansys also sell a Y-splitter for the mini-USB port Expansys UK. This will allow you to charge and use headphones at the same time, although if your headset has a right-angle connector you’ll probably need the 11pin-to-3.5mm (http://www.expansys.com/p.aspx?i=138247) socket adaptor too (allowing you to use any headphones), because the right-angled headphone connector covers up the power socket on Expansys’ splitter. The Cingular 8525 comes with a Y-splitter. All these adapters are available on eBay fairly cheap – just search for “JasJam Adapter”.
