What's the Trick to Proving tan3A=3tanA-tan^3 A/ 1-3tan^2 A?

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Homework Help Overview

The discussion revolves around proving the trigonometric identity involving the tangent function, specifically the equation tan(3A) = (3tan(A) - tan^3(A)) / (1 - 3tan^2(A)). The subject area is trigonometry, focusing on identities and transformations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster seeks assistance in proving the identity but encounters difficulties. One participant suggests using the tangent addition formula and proposes to set A = B to derive tan(2A) before finding tan(3A). Another participant shares their intermediate result but expresses uncertainty about their approach.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the proof. Some guidance has been offered regarding the use of the tangent addition formula, but there is no clear consensus on the correct path forward.

Contextual Notes

Participants are grappling with the steps involved in manipulating the identity and may be facing challenges in their algebraic transformations. The original poster expresses frustration at reaching a dead end, indicating potential gaps in understanding or execution of the method.

rhule009
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can anyone help[ me prove the following identity i keep on ending up in a dead end

tan3A=3tanA-tan^3 A/ 1-3tan^2 A
thank you
 
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you know that [tex]\tan(A+B) = \frac{\tan A + \tan B}{1-\tan A \tan B}[/tex]. Setting [tex]A = B[/tex] we get [tex]\tan 2A = \frac{2\tan A}{1-\tan A \ tan A}[/tex]. So what is [tex]\tan(A+2A)[/tex]? Thus work from the left to the right.
 
Last edited:
i end up with
tanA+2tanA/1-tanAtanAtanA
 
what am i doing wrong
 

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