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Proving these two angles are equal

  1. Oct 30, 2011 #1
    I'm researching an abstract geometric property and I've discovered the problem depends on showing these two angles are equal for strictly positive x:

    arctan(x) - arctan(x^3 +2x -((x^2 + 1)^(3/2)))

    and

    -arctan(x) + arctan(x^3 +2x + ((x^2 + 1)^(3/2)))

    Any help would be greatly appreciated, I've been trying this for hours and I think I'm stuck in a rut.

    Many Thanks!
     
  2. jcsd
  3. Oct 30, 2011 #2

    Ibix

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    Science Advisor

    Suggestion: take the tangent of each expression and use the formula for tan(A+B) to get a ratio of polynomials. Multiply top and bottom of each one by the denominator of the other expression to get them over a common denominator and multiply out the numerators.
     
  4. Oct 30, 2011 #3
    Thanks and we get tan of both are equal and we know both must be less than pi/2, problem solved!
     
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