Thank you for the nice explanation.
I see that you used the FullSimplify function and specified a certain range for x; then tested whether the 2 functions ArcTan and ArcSin are equal over that range. We see that the result is True.
Before I posted the question, I used Mathematica to test whether the functions ArcTan and ArcSin are equal, but I had not used the FullSimiplify function, or specified a range.
