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One way would be to wire a ~300 watts true sine inverter to your coach batteries that would feed just your TV and sound system. This could bypass the power distribution system already installed, be simple to use (you might have to plug & unplug a couple of power cords to use the inverter), and simple to install.
Another way would be to install a larger inverter, perhaps 1000 or 2000 watts, and make it part of the couches installed power system. This might require larger/better batteries, cost more to purchase and install but would allow you to run a microwave, a coffee pot, or other larger electrical appliance off your batteries along with your TV.
Others will make more suggestions, but the best way is what works for you!
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