Proving these two angles are equal

  • #1

Main Question or Discussion Point

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!
 

Answers and Replies

  • #2
Ibix
Science Advisor
Insights Author
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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.
 
  • #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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