Initial program 0.5
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
Initial simplification0.5
\[\leadsto \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{(v \cdot v + -1)_*}\right)\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \cos^{-1} \left(\frac{(\left(-5 \cdot v\right) \cdot v + 1)_*}{\color{blue}{1 \cdot (v \cdot v + -1)_*}}\right)\]
Applied add-sqr-sqrt0.6
\[\leadsto \cos^{-1} \left(\frac{\color{blue}{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*} \cdot \sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}}{1 \cdot (v \cdot v + -1)_*}\right)\]
Applied times-frac0.6
\[\leadsto \cos^{-1} \color{blue}{\left(\frac{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}{1} \cdot \frac{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}{(v \cdot v + -1)_*}\right)}\]
Simplified0.6
\[\leadsto \cos^{-1} \left(\color{blue}{\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*}} \cdot \frac{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}{(v \cdot v + -1)_*}\right)\]
- Using strategy
rm Applied add-exp-log0.6
\[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*} \cdot \frac{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}{(v \cdot v + -1)_*}\right)\right)}}\]
Final simplification0.6
\[\leadsto e^{\log \left(\cos^{-1} \left(\sqrt{(-5 \cdot \left(v \cdot v\right) + 1)_*} \cdot \frac{\sqrt{(\left(-5 \cdot v\right) \cdot v + 1)_*}}{(v \cdot v + -1)_*}\right)\right)}\]
