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

In summary, the equation for solving Arc Tangent Squared is tan(2x) - 3cot(2x) = 0. The value of x cannot be determined without more information. In this equation, tangent and cotangent are inverse trigonometric functions. There are multiple methods for solving this equation, including using trigonometric identities, substitution, or graphing. This equation can be solved using both analytical and numerical methods.
  • #1
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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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  • #2
Sure. Why not?
 
  • #3
so [arctan(3)]^2 = arctan(3) * arctan(3)

?
 
  • #4
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.
 

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

What is the equation for solving Arc Tangent Squared?

The equation for solving Arc Tangent Squared is tan(2x) - 3cot(2x) = 0.

What is the value of x in the equation tan(2x) - 3cot(2x) = 0?

The value of x in the equation tan(2x) - 3cot(2x) = 0 cannot be determined without more information. Additional context or equations are needed to solve for x.

What is the relationship between tangent and cotangent in this equation?

In this equation, tangent and cotangent are inverse trigonometric functions. This means that they are related in a way that allows for the equation to be solved using trigonometric identities and algebraic manipulation.

Is there a specific method for solving this equation?

Yes, there are multiple methods for solving this equation. Some possible methods include using trigonometric identities, substitution, or graphing the equation to find the points of intersection.

Can this equation be solved analytically or numerically?

This equation can be solved using both analytical and numerical methods. Analytical methods involve using algebra and trigonometric identities to manipulate the equation and find a solution. Numerical methods involve using numerical approximation techniques to find an approximate solution.

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