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trigsimp

trigsimp(2*cosa+2*sina);

Calculate

trigsimp

(x+a)^2;

trigsimp(%);

Calculate

trigsimp

trigsimp(%o1);

Calculate

trigsimp

trigsimp((1/(1+tg(x/2...

Calculate

trigsimp

(x+a)^2;

trigsimp((x+a)^2);

Calculate

trigsimp

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

Calculate

trigsimp

trigsimp(%o1);

Calculate

trigsimp

trigsimp(2*cosa+2*sina);

Calculate

trigsimp

Run Example
(%i1)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) define(N(t), trigsimp(uvect(Tp(t))));
                          10 cos(t)                2 sin(t)
(%o15)    N(t) := [- --------------------, - --------------------, 0]
                                2                       2
                     sqrt(96 cos (t) + 4)    sqrt(96 cos (t) + 4)
(%i16) 
Run Example
eq1:cos(phi)-cos(phi+dphi);
(%o1)                     cos(phi) - cos(phi + dphi)
(%i2) trigsimp(eq1);
(%o2)                     cos(phi) - cos(phi + dphi)
(%i3) 
Run Example
M: matrix ([-1, -0.2, 0], [1/(2*sqrt(y0)), -1, 0], [1, -exp(-y1), -1]);
                         [    - 1       - 0.2     0  ]
                         [                           ]
                         [     1                     ]
(%o1)                    [ ----------    - 1      0  ]
                         [ 2 sqrt(y0)                ]
                         [                           ]
                         [                 - y1      ]
                         [     1       - %e      - 1 ]
(%i2) B: matrix([-2*z0, -1, -1], [-1, 0, -1], [0, -2*z1, -1]);
                            [ - 2 z0   - 1    - 1 ]
                            [                     ]
(%o2)                       [  - 1      0     - 1 ]
                            [                     ]
                            [   0     - 2 z1  - 1 ]
(%i3) trigsimp(invert(M).M);

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced 0.1 by 1/10 = 0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.2 by -1/5 = -0.2

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.2 by -1/5 = -0.2

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced 0.1 by 1/10 = 0.1

rat: replaced -0.2 by -1/5 = -0.2

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced 0.1 by 1/10 = 0.1
                                  [ 1  0  0 ]
                                  [         ]
(%o3)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i4) 
[acos,matrix,phi,pi,plot2d,sin,sqrt,trigsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,solve,subst,trigsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,solve,trigsimp] [assume,constant,cos,declare,diff,let,letsimp,sin,subst,trigsimp] [assume,cos,diff,sin,solve,sqrt,subst,tan,trigsimp] [atan,logarc,logcontract,ratsimp,rectform,rhs,tan,trigsimp] [bfloat,diff,fpprec,solve,trigsimp] [coeff,cos,depends,diff,expand,factor,sin,solve,subst,trigsimp] [cos,cot,declare,defrule,evfun,false,let,letsimp,matchdeclare,sin,tan,tellsimp,trigexpand,trigsimp,true] [cos,cot,declare,evfun,false,let,letsimp,matchdeclare,sin,tan,tellsimp,trigexpand,trigsimp,true] [cos,cot,declare,evfun,let,letsimp,matchdeclare,sin,tan,tellsimp,trigexpand,trigsimp,true] [cos,declare,diff,halfangles,pi,radcan,solve,trigexpand,trigrat,trigsimp,true] [cos,define,diff,draw,draw3d,float,load,parametric,sin,trigsimp] [cos,define,diff,load,sin,sqrt,trigsimp] [cos,define,diff,load,sin,trigsimp] [cos,diff,display2d,false,ratsimp,sin,solve,subst,trigsimp] [cos,diff,display2d,false,sin,subst,trigsimp] [cos,diff,integrate,plot2d,trigexpand,trigrat,trigsimp] [cos,diff,ratsimp,sin,subst,trigsimp] [cos,diff,ratsimp,sin,trigsimp] [cos,diff,sin,string,trigsimp] [cos,diff,sin,subst,trigsimp] [cos,diff,sin,trigsimp] [cos,diff,string,trigsimp] [cos,diff,tan,trigsimp] [cos,diff,trigsimp] [cos,display2d,false,matrix,sin,trigsimp] [cos,display2d,false,sin,solve,trigreduce,trigsimp] [cos,expand,load,sin,trigreduce,trigsimp] [cos,expand,makelist,plot2d,random,sin,trigsimp] [cos,expand,trigexpand,trigreduce,trigsimp] [cos,invert,matrix,sin,trigreduce,trigsimp] [cos,load,sin,sqrt,trigexpand,trigrat,trigreduce,trigsimp] [cos,load,sin,trigexpand,trigsimp] [cos,sin,solve,trigsimp] [cos,sin,sqrt,trigsimp] [cos,sin,string,trigsimp] [cos,sin,trigexpand,trigsimp] [cos,sin,trigsimp] [cos,sqrt,trigexpand,trigsimp] [cos,trigsimp] [diff,sin,string,trigsimp] [exp,invert,matrix,sqrt,trigsimp] [exp,trigsimp] [integrate,radcan,ratsimp,trigsimp] [sin,trigexpand,trigsimp] [sin,trigsimp] [sqrt,trigreduce,trigsimp] [sqrt,trigsimp] [trigsimp]

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