Can anybody help me finding the proof for the Hyperbolic law of cosines:
cosh(c) = cosh(a).cosh(b) - sinh(a).sinh(b).cos(gamma)
I have been asked to prove the first law of cosines
cosh(c) = cosh(a).cosh(b) - sinh(a).sinh(b).cos(gamma)
I am told initially to proceed as follows:
Explain why I may assume that T is contained in D (The hyperbolic disk) and also why
V(c) = 0, V(a) = tanh(b/2) and V(b) = e^(i)(gamma)tanh(a/2)
Here V(a), V(b) and V(c) are all vertexes of the hyperbolic triangle with angles alpha, beta and gamma.
I didnt know how to draw the picture here. Anyway could anybody help me on this part of the problem
Thanks!