Initial program 31.9
\[\frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) + 1\right)}\]
Initial simplification24.4
\[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \tan k}}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
- Using strategy
rm Applied *-un-lft-identity24.4
\[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \tan k}}{\color{blue}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}\]
Applied tan-quot24.4
\[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \color{blue}{\frac{\sin k}{\cos k}}}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
Applied associate-*r/24.4
\[\leadsto \frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\color{blue}{\frac{\sin k \cdot \sin k}{\cos k}}}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
Applied associate-/r/24.4
\[\leadsto \frac{\color{blue}{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \sin k} \cdot \cos k}}{1 \cdot (\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
Applied times-frac24.4
\[\leadsto \color{blue}{\frac{\frac{\frac{2}{t} \cdot \left(\frac{\ell}{t} \cdot \frac{\ell}{t}\right)}{\sin k \cdot \sin k}}{1} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}\]
Simplified15.9
\[\leadsto \color{blue}{\frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}} \cdot \frac{\sin k}{\frac{\ell}{t}}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
- Using strategy
rm Applied *-un-lft-identity15.9
\[\leadsto \frac{\color{blue}{1 \cdot \frac{2}{t}}}{\frac{\sin k}{\frac{\ell}{t}} \cdot \frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
Applied times-frac13.9
\[\leadsto \color{blue}{\left(\frac{1}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}}}\right)} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\]
Applied associate-*l*12.5
\[\leadsto \color{blue}{\frac{1}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \left(\frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)}\]
Simplified12.5
\[\leadsto \color{blue}{\frac{\frac{\ell}{t}}{\sin k}} \cdot \left(\frac{\frac{2}{t}}{\frac{\sin k}{\frac{\ell}{t}}} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)\]
- Using strategy
rm Applied associate-*l/11.5
\[\leadsto \frac{\frac{\ell}{t}}{\sin k} \cdot \color{blue}{\frac{\frac{2}{t} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}}{\frac{\sin k}{\frac{\ell}{t}}}}\]
Applied associate-*r/11.5
\[\leadsto \color{blue}{\frac{\frac{\frac{\ell}{t}}{\sin k} \cdot \left(\frac{2}{t} \cdot \frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*}\right)}{\frac{\sin k}{\frac{\ell}{t}}}}\]
Final simplification11.5
\[\leadsto \frac{\left(\frac{\cos k}{(\left(\frac{k}{t}\right) \cdot \left(\frac{k}{t}\right) + 2)_*} \cdot \frac{2}{t}\right) \cdot \frac{\frac{\ell}{t}}{\sin k}}{\frac{\sin k}{\frac{\ell}{t}}}\]
