I have had seven travel trailers over the years and never a problem with an inverter. I am pretty sure they all had one so yes I think they must be pretty reliable.
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[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.
[SIGPIC]
..I also have a 427 Cobra replica with an aluminum chassis.