Fourier transform's sine and cosine count as N grows I remember reading that in (discrete) Fourier transform for signals with even numbered N for length, the sine and cosine count is equal. Is this correct?

A bit of analysis:

N=1, there is only DC offset, which is a cosine wave of unlimited length.

N=2, Now, in addition to the DC offset term there is a other wave. But it's also a cosine wave, since trying to represent a sine with 2 points becomes impossible as only the 0 values of it can be sampled.

N=3, Sine can be represented as well as cos so there are 1 cos, 1 sine of same frequency and the DC offset cosine.

N=4, 3 cos, 1 sine, 3rd bin added with only cos wave possible.
...

So to me it seems that there are always going to be more cosine waves than sines. Did I make a mistake?

The interpretation that DC offset is a cosine could perhaps be debated though, has there ever been debate over this term? The fact that it surpasses the boundaries of N is a bit mind boggling.
There is no Cos and Sine. There are frequencies that represent the original signal starting with 0 rate (DC), one cycle per the N points, 2 cycles per the N points... and so on. Depends of the actual best frequency estimator of the signal the pahse of the signal is determined.