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Homework Help: Need help simplifying a trigonometric equation; arctan(cot(x)), assuming 0<x<pi/2

  1. Mar 29, 2012 #1
    Hello, I need help trying to simplify the equation below, I believe it should be in terms of x and constants only, no trigonometry.

    "Simplify arctan(cot(x)), assuming 0<x<pi/2"

    After many attempted solutions and failures, my most recent attempt is below.

    let arctan(1/tanx) = u
    ==> tan u = 1/tanx
    ==> tan u*tan x = 1

    This is really the most I can get up to.

    Thanks Dylan.
  2. jcsd
  3. Mar 29, 2012 #2
    Is this associated with a trig substitution you did while solving an integral?
  4. Mar 29, 2012 #3
    No this not associated with any integration, the whole question that I was given is what is in the quotation marks.

    Thanks Dylan.
  5. Mar 29, 2012 #4
    The solution has been found "(Pi/2) - x", just realized that my many hours or stressing was because 'pi' was not written with a capital 'Pi' and syntax would not recognize it.

    Thanks Dylan.
  6. Mar 29, 2012 #5
    Draw a right triangle. Put x as one of the angles (but not the right angle.) Now, think of these things:

    1) cot = adj/opp
    2) tan = opp/adj

    Now, let y be the other non-right angle. What is the relationship between x and y? What is the relationship between cotx and tany?
  7. Mar 29, 2012 #6
    OK good. But do you understand it? Or did you just put it into mathematica or something?
  8. Mar 29, 2012 #7
    No I did understand it, I substituted 'cot x = tan(Pi/2 -x)' into my equation, which was my first attempt of many.
    Thanks anyway for your help,
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