Initial program 17.3
\[\left(\left(-2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1 + {\left(\frac{U}{\left(2 \cdot J\right) \cdot \cos \left(\frac{K}{2}\right)}\right)}^{2}}\]
Initial simplification7.7
\[\leadsto \sqrt{1^2 + \left(\frac{\frac{\frac{U}{2}}{J}}{\cos \left(\frac{K}{2}\right)}\right)^2}^* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
- Using strategy
rm Applied *-un-lft-identity7.7
\[\leadsto \sqrt{1^2 + \left(\frac{\frac{\frac{U}{2}}{J}}{\color{blue}{1 \cdot \cos \left(\frac{K}{2}\right)}}\right)^2}^* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
Applied div-inv7.8
\[\leadsto \sqrt{1^2 + \left(\frac{\color{blue}{\frac{U}{2} \cdot \frac{1}{J}}}{1 \cdot \cos \left(\frac{K}{2}\right)}\right)^2}^* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
Applied times-frac7.8
\[\leadsto \sqrt{1^2 + \color{blue}{\left(\frac{\frac{U}{2}}{1} \cdot \frac{\frac{1}{J}}{\cos \left(\frac{K}{2}\right)}\right)}^2}^* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
Simplified7.8
\[\leadsto \sqrt{1^2 + \left(\color{blue}{\frac{U}{2}} \cdot \frac{\frac{1}{J}}{\cos \left(\frac{K}{2}\right)}\right)^2}^* \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left(-2 \cdot J\right)\right)\]
Final simplification7.8
\[\leadsto \left(\left(J \cdot -2\right) \cdot \cos \left(\frac{K}{2}\right)\right) \cdot \sqrt{1^2 + \left(\frac{U}{2} \cdot \frac{\frac{1}{J}}{\cos \left(\frac{K}{2}\right)}\right)^2}^*\]
