Initial program 8.7
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification8.7
\[\leadsto (\left(\tan \left(\pi \cdot \ell\right)\right) \cdot \left(\frac{-1}{F \cdot F}\right) + \left(\pi \cdot \ell\right))_*\]
Taylor expanded around inf 8.2
\[\leadsto \color{blue}{\pi \cdot \ell - \frac{\sin \left(\pi \cdot \ell\right)}{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}}\]
- Using strategy
rm Applied clear-num8.2
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}}}\]
- Using strategy
rm Applied *-un-lft-identity8.2
\[\leadsto \pi \cdot \ell - \frac{1}{\frac{{F}^{2} \cdot \cos \left(\pi \cdot \ell\right)}{\color{blue}{1 \cdot \sin \left(\pi \cdot \ell\right)}}}\]
Applied times-frac8.2
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\frac{{F}^{2}}{1} \cdot \frac{\cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}}}\]
Simplified8.2
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\left(F \cdot F\right)} \cdot \frac{\cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}}\]
- Using strategy
rm Applied associate-*l*0.7
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{F \cdot \left(F \cdot \frac{\cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)}\right)}}\]
Final simplification0.7
\[\leadsto \pi \cdot \ell - \frac{1}{F \cdot \left(\frac{\cos \left(\pi \cdot \ell\right)}{\sin \left(\pi \cdot \ell\right)} \cdot F\right)}\]
