Comment #2 on issue 2949 by pr...@goodok.ru: trig functions do not return exact results for half angles
http://code.google.com/p/sympy/issues/detail?id=2949

Many, but they can have big length of the algebraic expression.

http://mathworld.wolfram.com/TrigonometryAngles.html
With SEE ALSO section

And additionally:

http://upload.wikimedia.org/wikipedia/ru/math/f/c/7/fc798fad887dbfc701c946dbf71a7f9b.png

http://upload.wikimedia.org/wikipedia/ru/math/c/1/1/c118a4c78936e31982193c87a6c8cd80.png

I think the automatic calculation have sense when there are no nested roots (or not more then two nested roots), for other - the additional method or the option must be used if it possible.

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