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 frac-add1.0
\[\leadsto 2 \cdot \cos \color{blue}{\left(\frac{\left(2 \cdot \pi\right) \cdot 3 + 3 \cdot \cos^{-1} \left(\frac{-g}{h}\right)}{3 \cdot 3}\right)}\]
Simplified1.0
\[\leadsto 2 \cdot \cos \left(\frac{\color{blue}{3 \cdot \left(\cos^{-1} \left(\frac{-g}{h}\right) + 2 \cdot \pi\right)}}{3 \cdot 3}\right)\]
- Using strategy
rm Applied associate-/r*1.0
\[\leadsto 2 \cdot \cos \color{blue}{\left(\frac{\frac{3 \cdot \left(\cos^{-1} \left(\frac{-g}{h}\right) + 2 \cdot \pi\right)}{3}}{3}\right)}\]
Simplified1.0
\[\leadsto 2 \cdot \cos \left(\frac{\color{blue}{\cos^{-1} \left(-1 \cdot \frac{g}{h}\right) + 2 \cdot \pi}}{3}\right)\]
- Using strategy
rm Applied mul-1-neg1.0
\[\leadsto 2 \cdot \cos \left(\frac{\cos^{-1} \color{blue}{\left(-\frac{g}{h}\right)} + 2 \cdot \pi}{3}\right)\]
Applied acos-neg1.0
\[\leadsto 2 \cdot \cos \left(\frac{\color{blue}{\left(\pi - \cos^{-1} \left(\frac{g}{h}\right)\right)} + 2 \cdot \pi}{3}\right)\]
Applied associate-+l-1.0
\[\leadsto 2 \cdot \cos \left(\frac{\color{blue}{\pi - \left(\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi\right)}}{3}\right)\]
Applied div-sub1.0
\[\leadsto 2 \cdot \cos \color{blue}{\left(\frac{\pi}{3} - \frac{\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi}{3}\right)}\]
Applied cos-diff0.0
\[\leadsto 2 \cdot \color{blue}{\left(\cos \left(\frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi}{3}\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi}{3}\right)\right)}\]
Final simplification0.0
\[\leadsto 2 \cdot \left(\cos \left(\frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi}{3}\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) - 2 \cdot \pi}{3}\right)\right)\]
