Solving Arc Tangent Squared: tan(2x) - 3cot(2x) = 0

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Homework Help Overview

The problem involves the equation tan(2x) - 3cot(2x) = 0, which is situated within the context of trigonometric identities and equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation into a form involving squared terms, questioning the existence of a squared arc tangent. Other participants engage with this idea, discussing the implications of squaring the arc tangent.

Discussion Status

Participants are exploring different interpretations of the problem, with some providing guidance on how to approach solving the equation by substituting variables. There is no explicit consensus on the best method yet.

Contextual Notes

There is a mention of trigonometric knowledge as a prerequisite, but no specific constraints or additional information are provided in the discussion.

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Homework Statement


tan(2x) - 3 cot (2x) = 0


Homework Equations



Trigonometry Knowledge.

The Attempt at a Solution



tan(2x) - 3cot(2x) = 0
tan(2x) - 3/tan(2x) = 0

[tan(2x)]^2 - 3 = 0

[tan(2x)]^2 = 3


Is there such thing as Arc Tangent that's squared??
 
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Sure. Why not?
 
so [arctan(3)]^2 = arctan(3) * arctan(3)

?
 
What you wrote is true, but it has nothing to do with how you'd solve the problem.

Try setting u=tan 2x, so your equation becomes u2=3. Then solve for u, and then solve for x.
 

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