Initial program 17.5
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified17.5
\[\leadsto \color{blue}{J \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U}\]
Taylor expanded around 0 0.4
\[\leadsto J \cdot \left(\color{blue}{\left(\frac{1}{3} \cdot {\ell}^{3} + \left(\frac{1}{60} \cdot {\ell}^{5} + 2 \cdot \ell\right)\right)} \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
Simplified0.4
\[\leadsto J \cdot \left(\color{blue}{\left(\ell + \left(\ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)\right)} \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
- Using strategy
rm Applied associate-*r*0.4
\[\leadsto \color{blue}{\left(J \cdot \left(\ell + \left(\ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right)} + U\]
Simplified0.4
\[\leadsto \color{blue}{\left(\left(\ell + \left(\ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)\right) \cdot J\right)} \cdot \cos \left(\frac{K}{2}\right) + U\]
Final simplification0.4
\[\leadsto \left(\left(\ell + \left(\ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)\right) \cdot J\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
