52Chapter 2•General Triangles§2.3Note that in any triangle△ABC, ifa=bthenA=B(why?), and so both sides of formula(2.17) would be 0 (since tan 0◦=0). This means thatthe Law of Tangents is of no help inCase 3 when the two known sides are equal. For this reason, and perhaps also because of thesomewhat unusual way in which it is used, the Law of Tangents seems to have fallen out offavor in trigonometry books lately. It does not seem to have any advantages over the Lawof Cosines, which works even when the sides are equal, requires slightly fewer steps, and isperhaps more straightforward.4Related to the Law of Tangents areMollweide’s equations:5Mollweide’s equations: For any triangle△ABC,a−bc=sin12(A−B)cos12C,and(2.21)a+bc=cos12(A−B)sin12C.(2.22)Note that all six parts of a triangle appear in both of Mollweide’s equations.For thisreason, either equation can be used to check a solution of a triangle.If both sides of theequation agree (more or less), then we know that the solution is correct.
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