The Number of Sine and Cosine Waves in an $ N $ Point DFT
There is no contradiction.   

Both cases you have information from $ -\frac{ Fs }{ 2 } $ to $ \frac{ Fs }{ 2 } $.

The representation using Cosine ans Sine functions is using Real Functions.
Those functions are symmetric as Real Valued functions.
Namely if you a coefficient for a Sine in a given frequency it is for sure have energy on the negative frequency as well (See the DFT / Fourier Transform of Sine and Cosine).
Namely using those functions all needed it to go from $ 0 $ to $ \frac{ Fs }{ 2 } $ as the negative value is implicit.  

On the other end, for the Complex Exponent the energy is one sided.
Hence you must go from $ -\frac{ Fs }{ 2 } $ to $ \frac{ Fs }{ 2 } $.