addition and subtraction formulas for tangent


The addition formula for tangent will be achieved via brute from the addition formulas for sine and cosine.

tan⁡(α+β)=sin⁡(α+β)cos⁡(α+β)=sin⁡α⁢cos⁡β+cos⁡α⁢sin⁡βcos⁡α⁢cos⁡β-sin⁡α⁢sin⁡β=sin⁡αcos⁡α⋅cos⁡βcos⁡β+cos⁡αcos⁡α⋅sin⁡βcos⁡βcos⁡αcos⁡α⋅cos⁡βcos⁡β-sin⁡αcos⁡α⋅sin⁡βcos⁡β=tan⁡α⋅1+1⋅tan⁡β1⋅1-tan⁡α⁢tan⁡β=tan⁡α+tan⁡β1-tan⁡α⁢tan⁡β

Note that tan is an odd functionMathworldPlanetmath, i.e. (http://planetmath.org/Ie) tan⁡(-x)=-tan⁡x. This fact enables us to obtain the subtraction formula for tangent.

tan⁡(α-β)=tan⁡(α+(-β))=tan⁡α+tan⁡(-β)1-tan⁡α⁢tan⁡(-β)=tan⁡α-tan⁡β1+tan⁡α⁢tan⁡β
Title addition and subtraction formulas for tangent
Canonical name AdditionAndSubtractionFormulasForTangent
Date of creation 2013-03-22 16:59:04
Last modified on 2013-03-22 16:59:04
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 8
Author Wkbj79 (1863)
Entry type Derivation
Classification msc 33B10
Classification msc 26A09
Synonym addition and subtraction formulae for tangent
Synonym addition formula for tangent
Synonym subtraction formula for tangent
Related topic AdditionFormula
Related topic DefinitionsInTrigonometry
Related topic AngleBetweenTwoLines
Related topic AdditionFormulas