Probably worthless

Let L be latitude (measured north/south as positive/negative) and Z be angle from zenith along the meridian for an astronomical object on the meridian (measured north/south as positive/negative), then obviously (when you draw a cross section diagram of the Earth) declination δ is 

         δ = Z + L
            where Z = (±)N/S(90°-AN/S) with upper/lower case
            for altitude AN/S measured positive from due north/south.
         So
         δ = (±)N/S(90°-AN/S) + L  and  AN/S = 90°+(±)N/S(L-δ)  and  L = δ + (±)N/S(AN/S-90°)

         The formula for the altitude of the NCP/SCP is
         AN/S = 90°+(±)N/S(L-(±)NCP/SCP90°)
         To be explicit:
         AN(NCP)=L                   AS(NCP)=180°-L
         AS(SCP)=180°+L              AS(SCP)=-L