In my opinion, you don't. You want a lie detector test because in your gut you don't trust him. His reaction (to try to learn how to beat it) and his obvious failing of the test combine to say that your gut is saying that with good reason. I don't see a future with someone who isn't going out of their way to SHOW you that you can trust them now. FYI - those tests, while by no means infallible do have controls for the NATURAL fear that even truth tellers will have when being put on the spot in such an unnatural situation. So saying that you "studied" how to beat it because you are a "bad test taker" is either the dumbest excuse I've ever heard (which should make you reconsider a future with him) or the most blatantly dishonest one I can imagine. Neither would make me want to stick it out.
Rather than focusing on his truthfulness (or lack thereof) maybe it might be a good time to consider your reasons for wanting to reconcile. it is a long, hard process even when the WS is being 100% honest and committed. It can be worth it it in some cases. There are some marriages that come out the other side strong and healthy. But it can also lead to a long period of pain and continued mistreatment with a WS who is still unwilling to own up to what they've done and commit to the self-reflection and change necessary to become a person of integrity. Make sure you know what you are fighting for BEFORE you put your all into it. If your marriage hasn't been happy or fulfilling for a very long time, or your husband seems to want to sweep it all under a rug and wants you to just "get over it" - I'd suggest reconsidering reconciliation efforts. If on the other hand, when you look back on your time together, you can honestly say that he's made you happy FAR more than he had made you sad, that he's supported you at critical moments when you needed him, has made you feel loved and cared for during long periods of your relationship - than it may be worth the hard work of reconciliation. You will never be able to turn his mind inside out. To KNOW with absolute certainty that you know everything you want/need to know. So you need to figure out what, if any, actions he can take that will show a true desire on HIS part to rebuild your trust. And if taking this poly was one of those - he failed. Not just because he failed the TEST - but because he tried to beat it. That is, in my eyes, still 100% dishonest behavior. Nothing that would make me feel good about the future. So sorry you are having to deal with this.
BS - Female
Married 27 years, one adult child DD May 2016 “When we are no longer able to change a situation, we are challenged to change ourselves.” - V Frankl