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Actually, this doesn't work in any but the nearly trivial case. If Sage has gotten to the point (in something like human notation) that f(t) = sqrt(64(sin^2(t)+cos^2(t))cos^2(8t) + (sin^2(t)+cos^2(t)+64)sin^2(8t) + 16cos^2(t) + 8(sin^2(t)+cos^2(t))sin(8t) + 64sin^2(8t)), then f.simplify makes no change, f.simplify_full expands everything down to sin(t) and cos(t) without ever noticing the sin^2+cos^2, f.simplify_real makes no change, f.simplify_trig does the same thing as f.simplify_full. In fact, the expression can be written as sqrt( (sin(8t)+4)^2+64).