Law of Tangents
The Law of Tangents is a rather obscure trigonometric identity that is sometimes used in place of its better-known counterparts, the law of sines and law of cosines, to calculate angles or sides in a triangle.
Statement
If and are angles in a triangle opposite sides and respectively, then
Proof
Let and denote , , respectively. By the Law of Sines, By the angle addition identities, as desired.
Problems
Introductory
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Intermediate
In , let be a point in such that bisects . Given that , and , find .
(Mu Alpha Theta 1991)
Olympiad
Show that .
(AoPS Vol. 2)