I have two lines of working that I am trying to understand.
First line:
\begin{equation}
\frac{(1+Z^{-1})\tan\frac{wc}{2}}{(1-Z^{-1})+(1+Z^{-1})\tan\frac{wc}{2}}
\end{equation}
Next line:
\begin{equation}
\frac{(1+Z^{-1})\tan\frac{wc}{2}}{(1+\tan\frac{wc}{2})-(1-\tan\frac{wc}{2})Z^{-1}}
\end{equation}
I know that they equal each other but I'm not sure how the denominator is transformed from one to the other. Am I missing some algebra trick?
Thanks for your help.
You can do the following.
$(1-z^{-1})+(1+z^{-1})\tan \frac{wc}{2} =1-z^{-1}+\tan \frac{wc}{2}+z^{-1}\tan \frac{wc}{2}=\\(1+\tan \frac{wc}{2})-z^{-1}+z^{-1}\tan \frac{wc}{2}=(1+\tan \frac{wc}{2})+(\tan \frac{wc}{2}-1)z^{-1}=\\(1+\tan \frac{wc}{2})-(1-\tan \frac{wc}{2})z^{-1} $
I've tried to do it in detail. There isnøt really any trick to it.