sidious vader vs obi wan part2

in a new hope vader and kenobi duel again why did sidous not help fight when vader lost last time sidious seemed concerned about him in rots after his fight with yoda why not help him this time

the emperor wasn't near the Death Star to make a quick stop to help out ... or he thought OB1 had died by now

Yes, remember that Tarkin believes Obi-Wan to be dead. So did Vader and the Emperor.

Which brings me to another question... Why the hell did they think that? Since Vader did get beaten by Obi Wan and hence he knows that he's alive,

I don't think there was anything after that in ROTS that suggests he did fake his death (like Yoda did)

Perhaps they thought he'd died of old age or something. They no longer felt his presence in the force so they probably thought it was because he was no longer around.

if not old age; the people don't really like the Jedi since they started the Clone Wars so chances are high he died by some locals