Calculate $\arctan x$ if $\arcsin x$ is known? I haven't been able to figure out using conventional identities, to calculate another if one is known. Say $\arcsin x$ is known, what is $\arctan x$ in terms of the former term?
This is not as easy as it looks.
How do I use the laws of trigonometry to solve this deceptively simple problem?

You can use the fact that $\sin(\arctan(x))) = \frac{x}{\sqrt{1+x^2}}$.
Therefore, $\arctan(x) = \arcsin(\sin(\arctan(x)) = \arcsin(\frac{x}{\sqrt{1+x^2}})$.
Edit: I just realized that I'm not using $\arcsin(x)$, but another value, so technically this answer is not very relevant.
