$5\mathrm{.}52$ Using the definition of Fourier transform, prove thatF $[$t f$($t$)]=$ jdd$\backslash$omega F$(\backslash$omega $).$Let the Fourier transform of f$($t$)$ beF$(\backslash$omega $)=1($A$+$ j$\backslash$omega $)$e$$j$\backslash$omega $+$B$.$Determine the Fourier transforms of the following signals $($setA $=2$ and B $=1).($a$)$ f

$($b$)$ f$($t$)$cos$($At

$($c$)$

f $/$dt