Initial program 13.4
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
Simplified10.5
\[\leadsto \color{blue}{F \cdot \frac{{\left(F \cdot F + \left(2 + x \cdot 2\right)\right)}^{\left(\frac{-1}{2}\right)}}{\sin B} - x \cdot \frac{1}{\tan B}}\]
- Using strategy
rm Applied associate-*r/10.5
\[\leadsto \color{blue}{\frac{F \cdot {\left(F \cdot F + \left(2 + x \cdot 2\right)\right)}^{\left(\frac{-1}{2}\right)}}{\sin B}} - x \cdot \frac{1}{\tan B}\]
Simplified10.5
\[\leadsto \frac{\color{blue}{F \cdot {\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{-1}{2}\right)}}}{\sin B} - x \cdot \frac{1}{\tan B}\]
- Using strategy
rm Applied distribute-frac-neg10.5
\[\leadsto \frac{F \cdot {\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\color{blue}{\left(-\frac{1}{2}\right)}}}{\sin B} - x \cdot \frac{1}{\tan B}\]
Applied pow-neg10.5
\[\leadsto \frac{F \cdot \color{blue}{\frac{1}{{\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{1}{2}\right)}}}}{\sin B} - x \cdot \frac{1}{\tan B}\]
Applied un-div-inv10.5
\[\leadsto \frac{\color{blue}{\frac{F}{{\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{1}{2}\right)}}}}{\sin B} - x \cdot \frac{1}{\tan B}\]
Taylor expanded around inf 10.5
\[\leadsto \frac{\frac{F}{{\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{1}{2}\right)}}}{\sin B} - \color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\]
Simplified10.5
\[\leadsto \frac{\frac{F}{{\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{1}{2}\right)}}}{\sin B} - \color{blue}{1 \cdot \left(\frac{x}{\sin B} \cdot \cos B\right)}\]
Final simplification10.5
\[\leadsto \frac{\frac{F}{{\left(F \cdot F + \left(2 + 2 \cdot x\right)\right)}^{\left(\frac{1}{2}\right)}}}{\sin B} - 1 \cdot \left(\frac{x}{\sin B} \cdot \cos B\right)\]
