A much cheaper option is 2 batteries (I use 2 6v, which is a popular choice) and instead of installing a big inverter I use a smaller inverter just for the TV. The smaller inverter is plugged in to the 12v outlet behind the TV so there is no wiring. $50 for the inverter and about $200 for the batteries.
You can’t run the coffee pot or the outlets, but for me the cost to benefit ratio makes it worthwhile. I run the generator in the morning for about an hour to make coffee and charge the batteries.
Pretty much everything else you need in the trailer runs on the 12v system.
Here is a video about my set up.
https://youtu.be/iaQZY_naOdE
And here is my inverter. A disclaimer about the inverter- it is rated for 300 watts but if you plug it into the 12v outlet on the trailer, that outlet is not rated for that much wattage. You can use it for the tv or small stuff, just not a hairdryer or big appliance.
https://www.amazon.com/BESTEK-300Wat.../dp/B07KQ4Q2L5