Given an irregular tetrahedron $ABCD$ with a circumscribed sphere. This defines $4$ spherical triangles. For the vertex $D$ these triangels are $ABD$, $BCD$ and $ACD$. How to prove that $$ \cos^2 ADB + \cos^2 BDC + \cos^2 ADC - 2 \cos ADB \cos BDC \cos ADC=1? $$
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1$\begingroup$ You are asking in the wrong forum. $\endgroup$– Gerald EdgarCommented Sep 12, 2022 at 19:33
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$\begingroup$ Can this be migrated to Math Stack Exchange? I would give an outline of how to get the answer there. $\endgroup$– Oscar LanziCommented Sep 13, 2022 at 12:27
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$\begingroup$ I have moved it to math.stackexchange.com/questions/4531153/…. $\endgroup$– kentCommented Sep 14, 2022 at 7:28
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