I am having difficulty in simplifying certain symbolc expressions in
Sage.  As I do not have much experience with this side of Sage it is
possible that there are some tricks I am missing.  Here are two
examples:

1. It is a fact that if a^2+b^2=1 then arcsin(a)+arcsin(b)=pi/2, but
how can I get this to happen automatically?  I have an expression
which comes out as

arcsin(1/3*sqrt(3)*sqrt(2)) + arcsin(1/3*sqrt(3))

which I would like to get simplified in this way.

2. I would like to get expressions like

sqrt(-t^2 + 1)*sqrt((2*t^2 - 1)/(t^2 - 1))

simplified to sqrt(1-2*t^2).  Using simplify_radical does something,
but not what I want:

I*sqrt(2*t^2 - 1)

which causes problems later on in the computation (where 1-2*t^2 is
known to be positive).

John

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