Speeding ticket... court or pay it

Okay i was pulled over in a 35 with a radar clocking me at 52. This happened on a hill where when you come down its a curve and cant really see whats ahead of you and officers wait in a corner and clock you as your coming down. No more than like 2 or 300 yards down the road the speed limit changes to 45 and there is a traffic light before that. So as i come down the hill i have my foot on the brake to stop at the light and when i make a left at the light the cop turns on his lights and pulls me over. He comes to the door and says im pulling you over for going 52 in a 35 and you had your foot on the brake so you probably were going faster than that. I reply i was on a hill so i was trying to slow down. He takes my info and brings back a ticket for 263 bucks and ask if i have any questions. Im so pissed i just say no sir and thanks and he walks away... should i try to fight this in court or just pay and go to traffic school...I just think he was being a little smart instead of professional..... ive only had one ticket before this but it was also for speeding on the interstate... could there be a way of getting it lowered?

Traffic school is your easiest way out, though it will cost you extra on top of the fine. If you went in to court and tried to explain yourself as you just did you would not do any good.
Hill or not, the speed limit is what it is.