What can I do if the cop issuing a traffic violation lied?

I was driving on the 405 freeway which has a speed limit of 65. I was in the carpool lane and my baby was sleeping in his carseat in the back. My speed was between 65-70 approximately. As I was driving, there was a cop in the far right lane, she switched all the way over and entered the carpool lane tightly behind me because I was trying to maintain the speed limit. After following me for about 5 minutes she stopped me and I was shocked and had no idea why. After I pulled over, she came up to my car and accussed me of speeding. She claimed I was driving 75 mph. There is NO WAY that I was going that speed. What I think happened was that she thought I was alone in the car and violating the carpool lane laws and pulled me over but then once she saw my son sleeping, she had to come up with an excuse and claimed I was going 75. I saw her behind me and there was no way any normal person would speed if a cop was following them. I tried to maintain my 65 speed but a person driving on the freeway, with their foot on the gas may have speed fluctuations between 65-70 and that is just normal! I didn't want to sign the ticket because it said I was going 75 but she told me I ahd to and that I could take it to court (which I will). She also said that she can give me a speeding ticket for going 66 when I protested that my speed was definitely less than 70. I told her that people don't usually drive with their cruise control on 65 on the freeway! It's not safe! So, what should I do? Will the judge believe me if I just tell the truth?