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, 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 .