Some points regarding trigonometric and inverse trigonometric functions in solveset :

There are many issues in solveset
solve_trig
.More inverse trigonometric formula and trigonometric identities should be defined/added or improved. Alsosimplify
,trigsimp
and insolveset
_invert
methods should be improved accordingly. 
Some links, that is helpful to improve these functions.

trigsimp
must be more powerful so thatsolve_trig
get simplified eq. (which solves trig equation by converting them into itsexp
form). 
solve_trig
solves the trig eq. using itsexp
form. There may be cases when thatexp
form is complicated and solveset fail to handle that form. There should be technique to convert that complicated form to simpler form(if possible) and then call thesolveset_complex
. That may help to improve thesolve_trig
method. 
We can use
_osbornei
,hyper_as_trig
methods defined insimplify/fu.py
to convert hyperbolic function to trigonometric function, then we can usetrigsimp
(we canâ€™t usetrigsimp
for hyperbolic functions). 
First need to improve basic concepts and add more identities. I opened a new PR to improve
rewrite
for trigonometric functions , PR is #11424.
eliminate() :

issue #2720 : We need some kind of eliminate function, like http://reference.wolfram.com/mathematica/ref/Eliminate.html. See also http://stackoverflow.com/q/20826969/161801

It looks something related to substitution function. But they are not same. Using
eliminate()
we will try to remove the variable(s) from the each equations(not solving the eq). 
Plan : First choose eq that have min. variables and get the value of the variable, to be eliminated. Go further and
subs
the value to next min. variable eq., and so on. 
Work in progress.
Meanwhile :

I found some basic issues in
ComplexInfinity
and trying to solve them in this PR #11409. 
there may be many things to be added about
ComplexInfinity
, one can refer this link to implement them : http://reference.wolfram.com/language/ref/ComplexInfinity.html.
continue..
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