2021-02-01 07:24:33 +0200 received badge ● Popular Question (source) 2013-07-21 06:53:30 +0200 asked a question Trigonometric simplification for distance on a sphere These are two equivalent equations for distance on a sphere: hav(x)=sin(x/2)^2 dist1(lat1, lat2, dLon)=2*asin(hav(lat1-lat2)+cos(lat1)*cos(lat2)*hav(dLon)) dist2(lat1, lat2, dLon)=acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(dLon))  (According to http://www.movable-type.co.uk/scripts... ) Indeed numerically they evaluate equal. But why their difference does not simplify to 0? diff(x,y,z)=dist1(x,y,z)-dist2(x,y,z) diff.simplify_full()  Am I doing something wrong? Is there a way to have Sage prove the two forms are equivalent, or to transform one to another? Thanks!