Would the Government tell us if they found Alien Life in or outside of Earth?

Or would there be a mass coverup?
Heres you better question added on as a beautiful side-dish
Why Would they cover up?…thats in addition to the other question.

That begs the questions whether the government would be the first to find alien life, and whether the aliens (if intelligent) would consent to having their existence covered up by Earthling governments.

The notion that Earthling governments would necessarily cover up the existence of aliens is a corollary to the "UFOs are alien spacecraft" theory. The proponents of that theory have to come up with an explanation for why, after decades of handwaving claims, there is no credible evidence for their claims. All they’ve come up with so far to explain the lack of evidence is that the government "must obviously" be covering it up. (I.e., it can’t possibly be that no such evidence exists, and therefore their claims are false.)

If you pay enough attention to some of the UFO enthusiasts, you discover that their motives are really about accusations of government coverup and have not much to do with whether there is scientific evidence of alien visitation. They just want an excuse to believe that authority is evil and deceptive.

EDIT 1:
The notion that the general public would necessarily panic at the revelation of alien life is part of the UFO mythos. As I said, the UFO enthusiasts need a hypothesis for why there’s no evidence of aliens. They speculate that the government’s hiding it. The next logical question is why they would do that. So the UFO enthusiasts — without any evidence — say it’s to keep people from panicking.

The typical argument revolves around Orson Welle’s radio program "War of the Worlds," which did induce panic (so the UFO people say) because it involved aliens. They conveniently forget that it involved an alien INVASION. People panicked because they thought the country was being invaded, not because there were allegedly aliens.

A brief perusal of fictional literature reveals a century-old treatment of space aliens. Clearly this is not an idea that bothers the majority of human beings. There’s no evidence that knowledge of aliens would raise a panic.