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Difference between revisions of "Tangent formula"

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A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form
 
A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092150/t0921501.png" /></td> </tr></table>
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$$\frac{a-b}{a+b}=\frac{\tan\frac 12(A-B)}{\tan\frac 12(A+B)}.$$
  
 
Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century.
 
Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century.
 
 
 
====Comments====
 
 
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  E.W. Hobson,  "Plane trigonometry" , Cambridge Univ. Press  (1925)  pp. 158</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''1–2''' , Springer  (1987)  (Translated from French)</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  E.W. Hobson,  "Plane trigonometry" , Cambridge Univ. Press  (1925)  pp. 158</TD></TR>
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Latest revision as of 18:13, 1 June 2023

A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form

$$\frac{a-b}{a+b}=\frac{\tan\frac 12(A-B)}{\tan\frac 12(A+B)}.$$

Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century.

References

[a1] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
[a2] E.W. Hobson, "Plane trigonometry" , Cambridge Univ. Press (1925) pp. 158
How to Cite This Entry:
Tangent formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_formula&oldid=15709
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article