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

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The equation tan(2x) - 3cot(2x) = 0 can be transformed into [tan(2x)]^2 - 3 = 0, leading to [tan(2x)]^2 = 3. This indicates that tan(2x) can be expressed as ±√3. To solve for x, it is suggested to set u = tan(2x), simplifying the equation to u^2 = 3. The final steps involve solving for u and subsequently for x, ensuring a clear path to the solution.
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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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