Initial program 16.1
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
Initial simplification15.8
\[\leadsto \pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}\]
- Using strategy
rm Applied associate-/r*12.1
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}}\]
- Using strategy
rm Applied *-un-lft-identity12.1
\[\leadsto \pi \cdot \ell - \frac{\color{blue}{1 \cdot \frac{\tan \left(\pi \cdot \ell\right)}{F}}}{F}\]
Applied associate-/l*12.1
\[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}}\]
Taylor expanded around 0 30.7
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\frac{{F}^{2}}{\pi \cdot \ell} - \frac{1}{3} \cdot \left({F}^{2} \cdot \left(\pi \cdot \ell\right)\right)}}\]
Simplified8.1
\[\leadsto \pi \cdot \ell - \frac{1}{\color{blue}{\left(\frac{\frac{F}{\pi}}{\ell} - \left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)\right) \cdot F}}\]
- Using strategy
rm Applied clear-num8.1
\[\leadsto \pi \cdot \ell - \frac{1}{\left(\frac{\color{blue}{\frac{1}{\frac{\pi}{F}}}}{\ell} - \left(\ell \cdot F\right) \cdot \left(\pi \cdot \frac{1}{3}\right)\right) \cdot F}\]
Final simplification8.1
\[\leadsto \pi \cdot \ell - \frac{1}{F \cdot \left(\frac{\frac{1}{\frac{\pi}{F}}}{\ell} - \left(\ell \cdot F\right) \cdot \left(\frac{1}{3} \cdot \pi\right)\right)}\]
