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 add-sqr-sqrt0.5
\[\leadsto \cos^{-1} \left(\frac{\color{blue}{\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*} \cdot \sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*}}}{v \cdot v - 1}\right)\]
Applied associate-/l*0.6
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*}}{\frac{v \cdot v - 1}{\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*}}}\right)}\]
Taylor expanded around 0 0.5
\[\leadsto \color{blue}{\cos^{-1} \left(\frac{(-5 \cdot \left({v}^{2}\right) + 1)_*}{{v}^{2} - 1}\right)}\]
Simplified0.5
\[\leadsto \color{blue}{\cos^{-1} \left(\frac{(\left(v \cdot v\right) \cdot -5 + 1)_*}{(v \cdot v + -1)_*}\right)}\]
Final simplification0.5
\[\leadsto \cos^{-1} \left(\frac{(\left(v \cdot v\right) \cdot -5 + 1)_*}{(v \cdot v + -1)_*}\right)\]
