Math, Verify

Cosx + SinxTanx = SecX

I have been looking at this for some time now and have no idea. I am more than likely doing something supid, but I just can't figure it out. Pre-Calculus by the way. 

cos(x) + sin(x)tan(x) = sec(x)
tan(x) = sin(x)/cos(x)
sec(x) = 1/cos(x)
cos(x) + sin²(x)/cos(x) = 1/cos(x)
cos²(x)/cos(x) + sin²(x)/cos(x) = 1/cos(x)
cos²(x) + sin²(x) = 1
nigger.