Question: How to simplify this trig expression

In a homework assignment on differential geometry, a student used Mathematica to calculate the torsion of a trefoil curve.  His result, using identical steps as mine, was significantly simpler than what I had gotten with Maple, although as we see in the attached workseet, they are mathematically equivalent.

Is there a way to coax Maple to reduce its result to something like my student has obtained?

My calculation

T1 := (-192*cos(t)^6 + 288*cos(t)^4 - 912*cos(t)^3 - 108*cos(t)^2 + 684*cos(t) - 54)/(4608*cos(t)^9 - 10368*cos(t)^7 + 6208*cos(t)^6 + 7776*cos(t)^5 - 9312*cos(t)^4 - 2440*cos(t)^3 + 3492*cos(t)^2 + 372*cos(t) - 1169);


The student's calculation

T2 := 6*(10+38*cos(3*t)+cos(6*t))/(975+70*cos(3*t)-194*cos(6*t) -18*cos(9*t));


simplify(T1 - T2);




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