I only have a Springdale TT, but the stereo that came as stock in it runs on 12V. Yours is probably different and may not, though. If your trailer didn't come with a TV, think about buying a TV that runs on 12V. Many do. I bought this-
Insignia TV
and don't require an inverter. In my situation, buying an inverter would be sort of ridiculous. If I had, I'd be changing the 12VDC from the batteries into 110VAC via the inverter. I'd plug the power cord from the TV into the inverter and the wall wart on the TV cord would change the 110VAC back to 12VDC to power the TV. Lots of wiring and $$ on my part to go from 12V to 12V. This might not be your situation.
I just made a 12V cable with a cigarette lighter plug at one end and the correct barrel plug for the TV on the other, and voila! Right now the cord is rather long to reach the outlet, but I'm putting a 12V socket near the TV soon.
If you already have the TV, you might check to see if there's a wall wart on the plug or if the power cord plugs into the back of the TV (the circuitry to change it to 12VDC may be built in the TV). If so, it may be 12V, but double check the input voltage on the back of the TV to be sure. Same goes for the stereo. Could be a lot easier to power them than you think.
Rick