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Trigonometric Addition Formulas

Basic definition

The trigonometric addition formulas are a set of formulas that express trigonometric functions of sums of angles in terms of the trigonometric functions of the original angles.

Detailed definition

Angle addition formulas express trigonometric functions of sums of angles α ± β in terms of functions of α and β. The fundamental formulas of angle addition in trigonometry are given by
sin(α + β) | = | sin α cos β + sin β cos α
sin(α - β) | = | sin α cos β - sin β cos α
cos(α + β) | = | cos α cos β - sin α sin β
cos(α - β) | = | cos α cos β + sin α sin β
tan(α + β) | = | (tan α + tan β)/(1 - tan α tan β)
tan(α - β) | = | (tan α - tan β)/(1 + tan α tan β).

Educational grade level

high school level (California trigonometry standard)

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