What is the Fourier Transform of $\rect(2Bt)\cos[{\omega}_Ct + k_fm(t_k)t] $?
I got the following as the solution:
$$\DeclareMathOperator{\sinc}{sinc} \frac{1}{2} \frac{1}{2B} \sinc(\frac{\omega+{\omega}_C+k_fm(t_k) +}{4B}) + \frac{1}{2} \frac{1}{2B} \sinc(\frac{\omega-{\omega}_C-k_fm(t_k) +}{4B})$$
However, in the book it is given as:
$$ \frac{1}{2} \sinc(\frac{\omega+{\omega}_C+k_fm(t_k) +}{4B}) + \frac{1}{2} \sinc(\frac{\omega-{\omega}_C-k_fm(t_k) +}{4B})$$
Wolfram alpha shows this: