The hyperbolic law of tangents is the identity
![(tanh[1/2(a-b)/R])/(tanh[1/2(a+b)/R])=(tan[1/2(A-B)])/(tan[1/2(A+B)]),](/images/equations/HyperbolicLawofTangents/NumberedEquation1.svg) |
for a hyperbolic triangle of curvature 
whose sides 
and 
are opposite the angles 
and 
, respectively. Here 
is the hyperbolic tangent
and 
is the tangent. The identity follows from the hyperbolic
law of sines and sum-to-product identities (Anderson 1999, pp. 146-151).
The natural term "hyperbolic law of tangents" is coined here by analogy
with the established hyperbolic laws of cosines and sines.
