Initial program 13.8
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
Simplified13.7
\[\leadsto \color{blue}{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot \frac{F}{\sin B} - \frac{x}{\tan B}}\]
- Using strategy
rm Applied div-inv13.7
\[\leadsto {\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot \color{blue}{\left(F \cdot \frac{1}{\sin B}\right)} - \frac{x}{\tan B}\]
Applied associate-*r*10.6
\[\leadsto \color{blue}{\left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B}} - \frac{x}{\tan B}\]
- Using strategy
rm Applied tan-quot10.6
\[\leadsto \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]
Applied associate-/r/10.6
\[\leadsto \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
- Using strategy
rm Applied div-inv10.7
\[\leadsto \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \color{blue}{\left(x \cdot \frac{1}{\sin B}\right)} \cdot \cos B\]
Applied associate-*l*10.7
\[\leadsto \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \color{blue}{x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)}\]
Taylor expanded around inf 10.6
\[\leadsto \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]
Final simplification10.6
\[\leadsto \frac{1}{\sin B} \cdot \left({\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}} \cdot F\right) - \frac{x \cdot \cos B}{\sin B}\]
