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.
If and are angles in a triangle opposite sides and respectively, then
Let and denote , , respectively. By the Law of Sines,
(In general, since is constant in a triangle, any ratio of linear combinations applied to lengths of sides is equal to the ratio of the same linear combinations applied to the sines of the angles of the same sides.)
By the angle addition identities, as desired.
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In , let be a point in such that bisects . Given that , and , find .
Show that .