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.

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

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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