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

  1. May 6, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove cot(x) - tan(x) = 2tan(2x)

    2. Relevant equations
    Trig identities

    3. 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?

    Attached Files:

  2. jcsd
  3. May 6, 2014 #2


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    Gold Member

    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.
  4. May 6, 2014 #3
    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.
  5. May 6, 2014 #4


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    Gold Member

    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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