Proving these two angles are equal

  • Thread starter oxygengiver
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In summary, the conversation discusses a problem related to an abstract geometric property that involves showing the equality of two angles for positive x values. The suggestion is to take the tangent of each expression and use the formula for tan(A+B) to get a ratio of polynomials. By multiplying the expressions by the denominator of the other, both can be simplified and solved. This approach leads to the conclusion that the tangent of both expressions are equal and the problem is solved.
  • #1
oxygengiver
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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!
 
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  • #2
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!
 

What is the definition of "equal" when it comes to angles?

The definition of equal angles is that they have the same measure or degree. This means that the two angles have the same amount of rotation or opening between their sides.

What are some ways to prove that two angles are equal?

There are various ways to prove that two angles are equal, such as using the Angle Addition Postulate, the Vertical Angles Theorem, or the Angle Bisector Theorem.

How can I visually determine if two angles are equal?

If two angles are equal, they will appear to have the same size when compared side by side or when superimposed on each other.

What is the importance of proving two angles are equal?

Proving that two angles are equal is important in geometry as it helps establish congruence between shapes and figures. It also allows us to make accurate measurements and calculations in real-life situations.

Can two angles be equal even if they have different measures?

No, two angles cannot be equal if they have different measures. The definition of equal angles states that they must have the same measure or degree.

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