Circumpolar Equation Derivation
There is nothing wrong with your explanation.  You could add some explanatory notes like $a_{min} = l-c$ and $a_{max}=l+c$. Also, I suggest that you put the equation $l+\delta = \frac{\pi}2-a_{min}$ on a separate line.   

It is very good to figure out these equations on your own. 

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Here is an alternative explanation with less algebra:


If you walk outside at night, you will notice that the north star has an elevation of $l$ degrees if your latitude is $l$.  
The north star does not move.  
The angular distance between stars does not change  (in the short term!).
In order for the a star to be circumpolar, it needs to be within $l$ degrees of the north star (otherwise it will dip below the horizon when its hour angle is 12 hours.)
So, the angle $\theta$ between the north star to a circumpolar star needs to be less than $l$.  That angle is $\theta=90^\circ-\delta = \pi/2 -\delta$ where $\delta$ is the declination of the star.  
Finally, 
$$
\begin{align} \theta &amp;\leq l\\
\pi/2 -\delta &amp;\leq l \\
\pi/2  &amp;\leq  \delta + l \\
\pi/2  - l &amp;\leq \delta. 
\end{align}
$$