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
\[\leadsto \color{blue}{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2}\]
- Using strategy
rm Applied distribute-frac-neg1.0
\[\leadsto \cos \left(\frac{\cos^{-1} \color{blue}{\left(-\frac{g}{h}\right)}}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied acos-neg1.0
\[\leadsto \cos \left(\frac{\color{blue}{\pi - \cos^{-1} \left(\frac{g}{h}\right)}}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied div-sub1.0
\[\leadsto \cos \left(\color{blue}{\left(\frac{\pi}{3} - \frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied associate-+l-1.0
\[\leadsto \cos \color{blue}{\left(\frac{\pi}{3} - \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)} \cdot 2\]
Applied cos-diff0.1
\[\leadsto \color{blue}{\left(\cos \left(\frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)} \cdot 2\]
Simplified0.1
\[\leadsto \left(\color{blue}{\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
- Using strategy
rm Applied frac-sub0.0
\[\leadsto \left(\cos \color{blue}{\left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{3 \cdot \frac{3}{2}}\right)} \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\color{blue}{\frac{9}{2}}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\color{blue}{1 \cdot \frac{3}{2}}}\right)\right) \cdot 2\]
Applied add-sqr-sqrt0.0
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\color{blue}{\sqrt{\pi} \cdot \sqrt{\pi}}}{1 \cdot \frac{3}{2}}\right)\right) \cdot 2\]
Applied times-frac0.0
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \color{blue}{\frac{\sqrt{\pi}}{1} \cdot \frac{\sqrt{\pi}}{\frac{3}{2}}}\right)\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - 3 \cdot \pi}{\frac{9}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \color{blue}{\sqrt{\pi}} \cdot \frac{\sqrt{\pi}}{\frac{3}{2}}\right)\right) \cdot 2\]
Final simplification0.0
\[\leadsto \left(\sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \sqrt{\pi} \cdot \frac{\sqrt{\pi}}{\frac{3}{2}}\right) \cdot \sin \left(\frac{\pi}{3}\right) + \frac{1}{2} \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right) \cdot \frac{3}{2} - \pi \cdot 3}{\frac{9}{2}}\right)\right) \cdot 2\]
