PlanetMath: addition and subtraction formulas for tangent

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addition and subtraction formulas for tangent

(Derivation)

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

$\begin{displaymath}\begin{array}{rl} \tan(\alpha+\beta) & =\displaystyle \frac{\... ...{ \tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta} \end{array}\end{displaymath}$

Note that $\tan$ is an odd function, i.e. $\tan(-x)=-\tan x$ . This fact enables us to obtain the subtraction formula for tangent.

$\displaystyle \tan(\alpha-\beta)=\tan(\alpha+(-\beta))=\frac{ \tan \alpha+\tan(... ...n \alpha \tan(-\beta)}=\frac{ \tan \alpha-\tan \beta}{1+\tan \alpha \tan \beta}$

"addition and subtraction formulas for tangent" is owned by Wkbj79.

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Other names:

addition and subtraction formulae for tangent, addition formula for tangent, subtraction formula for tangent

This object's parent.

Attachments:: convexity of tangent function (Result) by rspuzio
angle multiplication and division formulae for tangent (Result) by rspuzio

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Cross-references: odd function, addition formulas for sine and cosine
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This is version 5 of addition and subtraction formulas for tangent, born on 2007-04-25, modified 2007-06-25.
Object id is 9261, canonical name is AdditionFormulaForTangent.
Accessed 2628 times total.

Classification:

AMS MSC:	26A09 (Real functions :: Functions of one variable :: Elementary functions)
	33B10 (Special functions :: Elementary classical functions :: Exponential and trigonometric functions)

Pending Errata and Addenda

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