Low frequency response of a BJT amplifier.How is the cutoff frequency equal to \$ \frac{1}{2\pi (R_S+R_{in})C_{in}}\$ in fig 2
The answer is simple: The 3dB cut-off (fc) is NOT defined for the frequency fc that gives Vin=0.707*Vs. Instead, it is defined for the frequency fc where the filters output is 3dB BELOW the maximum output. 

For a simple R-C lowpass resp. C-R highpass this maximum is unity (for very low resp. very high frequencies). But in Fig.2 this maximum (for infinite frequencies) is Vin=Vs*Rin/(Rin+Rs)  .