I predict that next, Trump will investigate the curious fact that Hawaii supposedly joined the union in 1959, just two years before Obama was supposedly born. What if there is a massive conspiracy to hide the fact that those two dates were actually reversed? Sure, Obama was born in Hawaii but quite possibly before it was part of the union. He may as well have been born in Guam or the Philippines or just a life raft drifting in the middle of the Pacific.
Sadly, Trump's feelings of self-importance could only be enhanced by his essentially having ordered the president to prove something both obvious and already proven.[Kudos to Obama for timing his response to Trump just before the correspondent's dinner where he managed to downsize Donald's ego into a new, fun-size.]
Meanwhile, we can only hope that Obama eventually gives up on the unreasonable assumption that one can reason with unreasonable people. Even if he gets re-elected, his time in office is short. There is no sense wasting time placating the perpetually implacable.