Help, I think my husband may be fooling me into thinking I can't get pregnant...Is there any way that...?

Is there any way that he can have a vasectomy without my knowing and is there a pill (that is obviously not FDA approved) that he can obtain that will alter the efficacy of his sperm? I believe he is capable of this and I want to know all that I need to know. My last resort will be giving him a polygraph test. We have one child together and he absolutely opposed to having any more. His reason, "I am happy with just one."