Hello everybody and thanks for reading.

I have been trying to solve the following problem without success, so I am looking for some advices..

I have the following equation

arccos(x) = arctan( root(1 - x^2) / x)

So I have to prove if that 'identity' is valid and say for what values of x is valid.

Even when I am able to construct the triangle from the data, I don't know how to find the valid values for x.

So far I have constructed a triangle with opposite root(1-x^2), adjacent x and hypotenuse 1.

I also restricted the domain so 1-x^2 >= 0, x != 0 and -1 <= x <= 1 (for the root, denominator, and arccos respectively).

I also tried to prove the identity using the Pythagorean theorem from the data of the arctan ( opposite and adjacent), and I get that the hypotenuse is 1, which is the same the arccos says.

But I have seen the plot of both functions and I realized they are only equal for 0 < x <= 1 and I don't know how I could get there. Intersecting the restrictions I said I only get [-1,1] - {0}.

I have even thought I should intersect the ranges of those functions, but I don't think that is valid.

Thanks in advance and sorry for the long post