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 clear-num0.1
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \color{blue}{\frac{1}{\frac{\frac{3}{2}}{\pi}}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Applied *-un-lft-identity0.1
\[\leadsto \left(\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{\color{blue}{1 \cdot 3}} - \frac{1}{\frac{\frac{3}{2}}{\pi}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Applied associate-/r*0.1
\[\leadsto \left(\cos \left(\color{blue}{\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{1}}{3}} - \frac{1}{\frac{\frac{3}{2}}{\pi}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Applied frac-sub0.0
\[\leadsto \left(\cos \color{blue}{\left(\frac{\frac{\cos^{-1} \left(\frac{g}{h}\right)}{1} \cdot \frac{\frac{3}{2}}{\pi} - 3 \cdot 1}{3 \cdot \frac{\frac{3}{2}}{\pi}}\right)} \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\cos \left(\frac{\color{blue}{\frac{\frac{3}{2}}{\frac{\pi}{\cos^{-1} \left(\frac{g}{h}\right)}} - 3}}{3 \cdot \frac{\frac{3}{2}}{\pi}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\cos \left(\frac{\frac{\frac{3}{2}}{\frac{\pi}{\cos^{-1} \left(\frac{g}{h}\right)}} - 3}{\color{blue}{\frac{\frac{9}{2}}{\pi}}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Final simplification0.0
\[\leadsto 2 \cdot \left(\frac{1}{2} \cdot \cos \left(\frac{\frac{\frac{3}{2}}{\frac{\pi}{\cos^{-1} \left(\frac{g}{h}\right)}} - 3}{\frac{\frac{9}{2}}{\pi}}\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)\]
