Initial program 1.0
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
Simplified1.0
\[\leadsto \color{blue}{2 \cdot \cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\]
- Using strategy
rm Applied add-cube-cbrt1.0
\[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\right)}\]
Taylor expanded around 0 1.0
\[\leadsto 2 \cdot \left(\color{blue}{{\left({\left(\cos \left(0.333333333333333315 \cdot \left(\cos^{-1} \left(-1 \cdot \frac{g}{h}\right) + 2 \cdot \pi\right)\right)\right)}^{2}\right)}^{\frac{1}{3}}} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\right)\]
Simplified0.0
\[\leadsto 2 \cdot \left(\color{blue}{\sqrt[3]{{\left(\cos \left(\left(2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)\right) \cdot 0.333333333333333315\right)\right)}^{2}}} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\right)\]
Final simplification0.0
\[\leadsto 2 \cdot \left(\sqrt[3]{{\left(\cos \left(\left(2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)\right) \cdot 0.333333333333333315\right)\right)}^{2}} \cdot \sqrt[3]{\cos \left(\frac{2 \cdot \pi + \cos^{-1} \left(\frac{g}{-h}\right)}{3}\right)}\right)\]
