The best way to know for sure is to get a screen shot of an oscilloscope output of the waveform. Most inverter manufacturers are showing the waveform output on their website. Here is one that I tested in the lab to show what a stepped modified waveform looks like.
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The above inverter company (PowerJack) now makes these inverters as true sinewave. The plugs were universal plugs and not just euro plugs, as I was mistaken.
Of course pure sine wave looks like this:
Waveform shaping can certainly be done with an LC filter. You will need to play with the values of the components but you can certainly soften the waveform a bit. As for filtering enough to get a pure sine wave from a modified, it would require alot of testing. A laptp can run a large LCD/LED screen off the port in the back. Laptops now come with both VGA and HDMI output on them to run large monitors or even TV’s from the output.