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trigsimp

lsg1: solve_rec(T[n]=...

lsg1: trigsimp(lsg1);

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trigsimp

T(X):= X.(1/T12).T14...

trigsimp (X.(1/X));

Calculate

trigsimp

trigsimp(%o1);

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trigsimp

trigsimp((x-1/a-1/b) ...

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trigsimp

trigsimp((x-1/a-1/b) ...

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trigsimp

trigsimp((x-1)^2+(x+4...

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trigsimp

trigsimp((x-1/a-1/b) ...

Calculate

trigsimp

Run Example
(%i1)rt:tan(atan(1/2)+atan(1/3))=1;
                                   1         1
(%o1)                     tan(atan(-) + atan(-)) = 1
                                   2         3
(%i2) trigsimp(lhs(rt));
                                     1         1
                            sin(atan(-) + atan(-))
                                     2         3
(%o2)                       ----------------------
                                     1         1
                            cos(atan(-) + atan(-))
                                     2         3
(%i3)  logarc(lhs(rt));
                    %i                %i             %i                %i
            %i (log(-- + 1) - log(1 - --))   %i (log(-- + 1) - log(1 - --))
                    2                 2              3                 3
(%o3) - tan(------------------------------ + ------------------------------)
                          2                                2
(%i4) ratsimp(%);
(%o4)             
Run Example
trigsimp((cos(a)*cos(b)*cos(c)*cos(d) + cos(a)*cos(e)*cos(c)*cos(f) + cos(b)*cos(d)));
(%o1) cos(a) cos(c) cos(e) cos(f) + (cos(a) cos(b) cos(c) + cos(b)) cos(d)
(%i2) 
Run Example
r(t) := [10*cos(t),2*sin(t),t];
(%o1)                  r(t) := [10 cos(t), 2 sin(t), t]
(%i2) r(4);
(%o2)                      [10 cos(4), 2 sin(4), 4]
(%i3) float(r(4));
(%o3)           [- 6.536436208636119, - 1.513604990615856, 4.0]
(%i4) load(draw);
(%o4)            /usr/share/maxima/5.21.1/share/draw/draw.lisp
(%i5) draw3d(color=magenta,parametric(-cos(t), sin(t),cos(t), t,-4, 4));
plotdraw3d(color=magenta,parametric(-cos(t), sin(t),cos(t), t,-4, 4));define(rp(t), diff(r(t), t));
(%o6)                 rp(t) := [- 10 sin(t), 2 cos(t), 1]
(%i7) float(rp(1));
(%o7)            [- 8.414709848078966, 1.08060461173628, 1.0]
(%i8) load(eigen);
(%o8)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i9) uvect(rp(t));
                     10 sin(t)                          2 cos(t)
(%o9) [- ---------------------------------, ---------------------------------, 
                     2           2                      2           2
         sqrt(100 sin (t) + 4 cos (t) + 1)  sqrt(100 sin (t) + 4 cos (t) + 1)
                                                             1
                                             ---------------------------------]
                                                         2           2
                                             sqrt(100 sin (t) + 4 cos (t) + 1)
(%i10) trigsimp(rp(t));
(%o10)                    [- 10 sin(t), 2 cos(t), 1]
(%i11) define(T(t), trigsimp(rp(t)));
(%o11)                T(t) := [- 10 sin(t), 2 cos(t), 1]
(%i12) define(Tp(t), diff(T(t), t));
(%o12)               Tp(t) := [- 10 cos(t), - 2 sin(t), 0]
(%i13) uvect(Tp(t));
                    10 cos(t)                        2 sin(t)
(%o13) [- -----------------------------, - -----------------------------, 0]
                    2             2                  2             2
          sqrt(4 sin (t) + 100 cos (t))    sqrt(4 sin (t) + 100 cos (t))
(%i14) trigsimp(uvect(Tp(t)));
                      10 cos(t)                2 sin(t)
(%o14)        [- --------------------, - --------------------, 0]
                            2                       2
                 sqrt(96 cos (t) + 4)    sqrt(96 cos (t) + 4)
(%i15) 
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