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Law of Tangents Theorem, Sine and Cosine Triange Angles Proof

The theorem determines the relationship between the tangents of two angles of a plane triangle and the length of the opposite sides. It can be proved using the law of sine and cosine of triangle angles.

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Law of Tangents Theorem, Sine and Cosine Triangle Angles

Statement:
If A and B are angles in a triangle having a and b as its opposite sides respectively,
then

Proof:
Let s be denoted as (A+B)/2 and d be denoted as (A-B)/2 respectively.

Law of Tangents can be proved from the Law of sines

By the angle of addition identities

  
   
  
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