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Inspired by the question here. I wanted to ask if someone knows that there is an invisible creature in front of him can the person declare an attack on something behind the invisible creature in order to hit the invisible creature without suffering the disadvantage that would have come with aiming at the invisible creature using the optional cover rules? Would it make a difference if the thing aimed at is a living thing or an object?

If you are using the optional rule mentioned there and your DM does not say "Nope you can't do this, too cheesy" using Rule 0, yes, you can. But yeah, the DM can veto this independent of the rules if he finds it too abusable.

There are a few caveats here that might disappoint you, though.

If a creature is providing cover for the missed creature and the attack roll exceeds the AC of the covering creature, the covering creature is hit.

So, you only hit the invisible creature if you miss the original target and the attack roll exceeds the invisible creature AC. If the invisible creature has an AC higher than the target+2, for example, it actually becomes impossible to hit the invisible creature and attacking with disadvantage would be better (you always have at least a 0.25% chance of hitting). In other scenarios, it still might be better to attack with disadvantage than attack normally and only hit if you fail to hit the actual target.

It's also unclear how the DM will rule the attack if your target is, for example, a wall. He could rule that you always hit the wall and not even roll an attack.

Finally, your DM might ask you why you are targeting some random stuff (if it's an object) instead of the invisible creature (which presumably is the actual target). If your table is fine with this kind of metagame, it won't be a problem, otherwise you might have some hard time explaining why you decided to target the vase behind the invisible creature instead of trying to hit the actual creature.

TL;DR: The rules do allow it, but your DM might not allow it, and personally if I am the DM I can't think of a reason to allow it consistently (i.e. not a one time thing for the lulz) because it seems just... cheesy?

No.

Because disadvantage is a mechanic, not something you 'avoid' in-character. The roll is the same in either case. PCs do not have concepts of the mechanics as mechanics, unless you're playing Deadpool.