Derive formula

$h_{bp}[n]=2\frac{sin{}_c(n-n_d)}{(n-n_d)}cos{}_{0}n$

for the impulse response of an ideal bandpass filter by :

$($a$)$ using the impulse response

$h_{1p}[n]=\frac{sin{}_c(n-n_d)}{(n-n_d)}$

of the ideal lowpass filter and the modulation property of DTFT$,$

$($b$)$ expressing the frequency response of the ideal bandpass filter as the difference between the frequency responses of two ideal lowpass filters.