In generalised trigonometry, a corollary for the law of sines in a tetrahedron with vertices A,B,C and D is defined as being: sin (angle DAB) multiplied by sin (angle DBC) multiplied by sin (angle DCA) = sin(angle DAC) multiplied by sin(angle DCB) multiplied by sin(angle DBA)
The generalised law of sines applies to a unidirectional, with length S in a space of any number dimensions, with constant Gaussian curvature K. With dimensional Euclidean space, we define this as being:
gsin S = S - KS to the power of 3/ 3! + K squared, S to the power of 5/5!...
However, how would the generalised law of tangents work in a specific number of dimensions. Could someone kindly provide me with some intuition on the subject of generalised trigonometry, for I am unable to fully comprehend it?