Trig identities, prove (cot(x)-tan(x)=2tan(2x))

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Homework Help Overview

The discussion revolves around proving the trigonometric identity cot(x) - tan(x) = 2tan(2x). Participants are examining the validity of this identity within the context of trigonometric identities.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the equality of the two sides of the equation, with some suggesting that the right-hand side may actually be 2cot(2x) instead of 2tan(2x). Others have tested specific values, such as x=π/4, to explore the identity's validity.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and interpretations. Some have expressed doubt about the original equation being correct, while others are considering the possibility of it being a trick question or a mistake. There is no explicit consensus on the identity's validity yet.

Contextual Notes

Participants mention that the homework requires full working with identities, which may influence their approaches. There is also uncertainty about whether the problem is intended to be a straightforward proof or if it involves specific conditions for certain values of x.

noahsdev
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Homework Statement


Prove cot(x) - tan(x) = 2tan(2x)


Homework Equations


Trig identities
http://en.wikipedia.org/wiki/List_of_trigonometric_identities

The Attempt at a Solution


I have worked it down and don't think they are equal. I think it's supposed to be 2cot(2x) not 2tan(2x), that is what I found. Am I correct or what have I done wrong?
Thanks
 

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Yes, I get the same result as you, although your calculation was a lot more complicated. If you let x=π/4, the LHS is zero while the RHS is undefined. So it cannot be 2tan(2x) for the equation to be an identity.
 
Thanks for the fast reply, my teacher wanted full working with identities so that's why it's in long form. I am not sure if it is a mistake or if it is a trick question, thanks.
 
noahsdev said:
Thanks for the fast reply, my teacher wanted full working with identities so that's why it's in long form. I am not sure if it is a mistake or if it is a trick question, thanks.
Most likely a mistake unless the question wanted you to find what particular subset of x satisfies the equation. But if it says 'Prove..' then that is not the case.
 

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