Proving these two angles are equal

[oxygengiver]

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!

 

[Ibix]

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.

 

[oxygengiver]

Thanks and we get tan of both are equal and we know both must be less than pi/2, problem solved!