Initial program 16.9
\[\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)\right) \cdot R\]
Initial simplification16.9
\[\leadsto R \cdot \cos^{-1} \left(\cos \left(\lambda_1 - \lambda_2\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \sin \phi_2 \cdot \sin \phi_1\right)\]
- Using strategy
rm Applied cos-diff3.7
\[\leadsto R \cdot \cos^{-1} \left(\color{blue}{\left(\cos \lambda_1 \cdot \cos \lambda_2 + \sin \lambda_1 \cdot \sin \lambda_2\right)} \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \sin \phi_2 \cdot \sin \phi_1\right)\]
- Using strategy
rm Applied associate-*r*3.7
\[\leadsto R \cdot \cos^{-1} \left(\color{blue}{\left(\left(\cos \lambda_1 \cdot \cos \lambda_2 + \sin \lambda_1 \cdot \sin \lambda_2\right) \cdot \cos \phi_1\right) \cdot \cos \phi_2} + \sin \phi_2 \cdot \sin \phi_1\right)\]
- Using strategy
rm Applied add-log-exp3.8
\[\leadsto R \cdot \color{blue}{\log \left(e^{\cos^{-1} \left(\left(\left(\cos \lambda_1 \cdot \cos \lambda_2 + \sin \lambda_1 \cdot \sin \lambda_2\right) \cdot \cos \phi_1\right) \cdot \cos \phi_2 + \sin \phi_2 \cdot \sin \phi_1\right)}\right)}\]
Final simplification3.8
\[\leadsto R \cdot \log \left(e^{\cos^{-1} \left(\sin \phi_2 \cdot \sin \phi_1 + \left(\cos \phi_1 \cdot \left(\cos \lambda_2 \cdot \cos \lambda_1 + \sin \lambda_2 \cdot \sin \lambda_1\right)\right) \cdot \cos \phi_2\right)}\right)\]
