See this is where people are often wrong… the officer does NOT have to show you the radar, in fact the officer does not even have to have you on radar to claim you are speeding as they use other methods to judge speeds as well.
I would agree that either way the cop could lie (claiming you are speeding when infact you are not) but in court, the judge will believe the cop unless you can give him reason not too (which normally does happen).
Now, when you fight tickets in court they look at your record very closely, if you have a clean record and this is your first ticket (then they sometimes drop it, or usually lower it atleast) but if you have a history or speeding etc, then they normally will not help you out.
Last thing… Sometimes cops do give out “bogus” tickets, and they know they are given out wrongfully but 75% of the time people just pay them. BUT when an officer KNOWS hes given out a wrongful ticket, luckly hood of him showing up in court to fight it is slim as shit (and ALWAYS REMEMBER THIS) Officers get paid overtime to show up in court and the reason they pay them overtime is so that they will indeed show up.