Trigonometry/For Enthusiasts/Less-Used Trig Identities

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Triangle Identities[edit]

In addition to the Law of Sines, the Law of Cosines, and the Law of Tangents, there are numerous other identities that apply to the three angles A, B, and C of any triangle (where A+B+C=180° and each of A, B, and C is greater than zero). Some of the most notable ones follow:


These are all direct consequences of Pythagoras's theorem.

Sum/Difference of angles[edit]

Product to Sum[edit]

Sum and difference to product[edit]

, where and

Multiple angle[edit]

These are all direct consequences of the sum/difference formulae

Half angle[edit]

In cases with , the sign of the result must be determined from the value of . These derive from the formulae.

Power Reduction[edit]