Kernel Crash

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That indicates there is something broken in your installation. The expected output is:

sage: f =cos(x)^2+sin(x)^2
sage: f
cos(x)^2 + sin(x)^2
sage: f.full_simplify()
1

The first thing to try is to reinstall sage, since this indicates something rather fundamental is broken (at least for the maxima/lisp subsystem that is used for simplification). If that doesn't help, you might get help by giving exact details about your operating system and the way you've installed sage. https://groups.google.com/forum/#!for... is probably a better forum to get help for this.