Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Simplified0.5
\[\leadsto \color{blue}{\cos^{-1} \left(\frac{(-5 \cdot \left(v \cdot v\right) + 1)_*}{v \cdot v - 1}\right)}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \cos^{-1} \left(\frac{\color{blue}{1 \cdot (-5 \cdot \left(v \cdot v\right) + 1)_*}}{v \cdot v - 1}\right)\]
Applied associate-/l*0.5
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{1}{\frac{v \cdot v - 1}{(-5 \cdot \left(v \cdot v\right) + 1)_*}}\right)}\]
Taylor expanded around 0 0.7
\[\leadsto \cos^{-1} \color{blue}{\left(\left(4 \cdot {v}^{4} + 4 \cdot {v}^{2}\right) - 1\right)}\]
Simplified0.7
\[\leadsto \cos^{-1} \color{blue}{\left((\left((\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(v \cdot v\right))_*\right) \cdot 4 + -1)_*\right)}\]
Final simplification0.7
\[\leadsto \cos^{-1} \left((\left((\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(v \cdot v\right))_*\right) \cdot 4 + -1)_*\right)\]
