In trigonometry, the law of tangents is a statement about arbitrary triangles in the plane. If two sides of a triangle are (lower-case) a and b and the angles opposite those sides are (capital) A and B, then the law of tangents states

Derivation

Start with (a + b)/(a - b). ((sin A)/a = (sin B)/b because of the law of sines):

(See: Trigonometric identity)