Initial program 1.0
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
- Using strategy
rm Applied add-cbrt-cube1.5
\[\leadsto 2 \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\right) \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)}}\]
Applied simplify1.0
\[\leadsto 2 \cdot \sqrt[3]{\color{blue}{{\left(\cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)\right)}^{3}}}\]
- Using strategy
rm Applied unpow31.5
\[\leadsto 2 \cdot \sqrt[3]{\color{blue}{\left(\cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)\right) \cdot \cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)}}\]
Applied cbrt-prod0.1
\[\leadsto 2 \cdot \color{blue}{\left(\sqrt[3]{\cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right) \cdot \cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)} \cdot \sqrt[3]{\cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)}\right)}\]
Applied simplify0.1
\[\leadsto 2 \cdot \left(\color{blue}{\sqrt[3]{\cos \left(\frac{\pi + \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \cdot \cos \left(\frac{\pi + \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)}} \cdot \sqrt[3]{\cos \left(\left(\frac{\pi}{3} + \frac{\pi}{3}\right) + \frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}\right)}\right)\]
