The Cosine Rule for Hyperbolic Triangles For any h-triangle ABC, sinh(b)sinh(c)cos(A) = cosh(b)cosh(c) - cosh(a), with similar formulae for cos(B) and cos(C).
Proof |
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assume that A is O, and that B is on the positive real axis. As A = O, AB and AC are line segments, making the angle A.
Thus the complex coordinates of A, B and C are 0, r and seiA,
From (3), This immediately gives the required result.
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by the Basic Strategy |