How to convert arctan to arcsin?

Question:How to convert arctan to arcsin?

Posted: Rouben Rostamian 8003 Product: Maple

August 17 2017

I am stumped with this trivial puzzle. Let
z := arctan(x/sqrt(a^2-x^2));

How do we simplify z to.

I tried all sorts of tricks with simplify(...) and convert(...), with assumptions, but did not get anywhere. Any clues?

Versions: Maple 2016 and 2017.

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