Problem $2(10$ Points$)$

Suppose the signal $x(t)=cos(210t)+cos(225t)$ is sampled at a rate of $f_{s}Hz.$ The sampled signal is then passed through a lowpass filter with impulse response $h(t)=\frac{sin24t}{t}.$ Determine the value of $f_s$ such that the filter output is of the form $cos(210t)+A,$ where $A$ is a non$-$zero constant.