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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).
The first four of these are known as the prosthaphaeresis formulas, or sometimes as Simpson's formulas.

    Educational grade level

    high school level (California trigonometry standard)

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