Initial program 17.0
\[\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)\right) \cdot R\]
Applied simplify17.0
\[\leadsto \color{blue}{\cos^{-1} \left((\left(\cos \phi_2 \cdot \cos \phi_1\right) \cdot \left(\cos \left(\lambda_1 - \lambda_2\right)\right) + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right) \cdot R}\]
- Using strategy
rm Applied sub-neg17.0
\[\leadsto \cos^{-1} \left((\left(\cos \phi_2 \cdot \cos \phi_1\right) \cdot \left(\cos \color{blue}{\left(\lambda_1 + \left(-\lambda_2\right)\right)}\right) + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right) \cdot R\]
Applied cos-sum3.7
\[\leadsto \cos^{-1} \left((\left(\cos \phi_2 \cdot \cos \phi_1\right) \cdot \color{blue}{\left(\cos \lambda_1 \cdot \cos \left(-\lambda_2\right) - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right)} + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right) \cdot R\]
Applied simplify3.7
\[\leadsto \cos^{-1} \left((\left(\cos \phi_2 \cdot \cos \phi_1\right) \cdot \left(\color{blue}{\cos \lambda_1 \cdot \cos \lambda_2} - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right) + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right) \cdot R\]
- Using strategy
rm Applied add-log-exp3.7
\[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left((\left(\cos \phi_2 \cdot \cos \phi_1\right) \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2 - \sin \lambda_1 \cdot \sin \left(-\lambda_2\right)\right) + \left(\sin \phi_2 \cdot \sin \phi_1\right))_*\right)}\right)} \cdot R\]
Applied simplify3.7
\[\leadsto \log \color{blue}{\left(e^{\cos^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}\right)} \cdot R\]
- Using strategy
rm Applied acos-asin3.8
\[\leadsto \log \left(e^{\color{blue}{\frac{\pi}{2} - \sin^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}}\right) \cdot R\]
Applied exp-diff3.8
\[\leadsto \log \color{blue}{\left(\frac{e^{\frac{\pi}{2}}}{e^{\sin^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}}\right)} \cdot R\]
Applied simplify3.8
\[\leadsto \log \left(\frac{\color{blue}{\sqrt{e^{\pi}}}}{e^{\sin^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_1 \cdot \sin \lambda_2\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}}\right) \cdot R\]
Taylor expanded around 0 3.8
\[\leadsto \color{blue}{\log \left(\sqrt{e^{\pi}} \cdot \frac{1}{e^{\sin^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_2 \cdot \sin \lambda_1\right))_*\right) \cdot \left(\cos \phi_2 \cdot \cos \phi_1\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)}}\right)} \cdot R\]
Applied simplify4.0
\[\leadsto \color{blue}{(\left(-R\right) \cdot \left(\sin^{-1} \left((\left((\left(\cos \lambda_1\right) \cdot \left(\cos \lambda_2\right) + \left(\sin \lambda_2 \cdot \sin \lambda_1\right))_*\right) \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\sin \phi_1 \cdot \sin \phi_2\right))_*\right)\right) + \left(\log \left(\sqrt{e^{\pi}}\right) \cdot R\right))_*}\]
