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trigexpand

f:(sin*(x+y));

p: trigexpand(f);

Calculate

trigexpand

trigexpand(sin3x);

Calculate

trigexpand

q : trigexpand(p);

Calculate

trigexpand

trigexpand(sin2*x);

Calculate

trigexpand

trigexpand(3*x);

Calculate

trigexpand

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

trigexpand

trigexpand(sin2*x);

Calculate

trigexpand-trigsimp

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

trigexpand-trigsimp

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

trigexpand

p:(sin*(1*x+y));

trigexpand (p);

Calculate

trigexpand

Run Example
(%i1)eq: ratsubst(sin(a)^2,1-cos(a)^2,trigexpand(cos(9*a)));
                    8                    6                    4
(%o1) 256 cos(a) sin (a) - 448 cos(a) sin (a) + 240 cos(a) sin (a)
                                                                  2
                                                   - 40 cos(a) sin (a) + cos(a)
(%i2) 
Run Example
expr : (x - a)^2*(y - b)*(z - c);
                                  2
(%o1)                      (x - a)  (y - b) (z - c)
(%i2) expand(expr);
       2                    2          2                  2          2
(%o2) x  y z - 2 a x y z + a  y z - b x  z + 2 a b x z - a  b z - c x  y
                                            2            2                2
                             + 2 a c x y - a  c y + b c x  - 2 a b c x + a  b c
(%i3) expr : (y + 1)^3/(y+1)^2;
(%o3)                                y + 1
(%i4) expand(expr);
(%o4)                                y + 1
(%i5) factor(126);
                                       2
(%o5)                               2 3  7
(%i6) factor(x^3 - 1);
                                       2
(%o6)                        (x - 1) (x  + x + 1)
(%i7) factor(2^63 - 1);
                           2
(%o7)                     7  73 127 337 92737 649657
(%i8) factor(-8*y - 4*x + z^2*(2*y + x));
(%o8)                      (2 y + x) (z - 2) (z + 2)
(%i9) ex : (3+x)*(2+2*x)/(1-x^2);
                               (x + 3) (2 x + 2)
(%o9)                          -----------------
                                         2
                                    1 - x
(%i10) fullratsimp(ex);
                                     2 x + 6
(%o10)                             - -------
                                      x - 1
(%i11) ex : ((x^(a/2) - 1)^2*(x^(a/2) + 1)^2)/(x^a - 1);
                              a/2     2   a/2     2
                            (x    - 1)  (x    + 1)
(%o11)                      -----------------------
                                     a
                                    x  - 1
(%i12) fullratsimp(ex);
                                     a
(%o12)                              x  - 1
(%i13) fullratsimp(ex);
                                     a
(%o13)                              x  - 1
(%i14) exp : (sin(x))^2 + 3* (cos(x))^2;
                                 2           2
(%o14)                        sin (x) + 3 cos (x)
(%i15) trigexpand(exp);
                                 2           2
(%o15)                        sin (x) + 3 cos (x)
(%i16) form : (cos(x))^4 + (cos(x))^3 + (cos(x))^2 + cos(x) + 1;
                      4         3         2
(%o16)             cos (x) + cos (x) + cos (x) + cos(x) + 1
(%i17) trigreduce(form);
       cos(4 x) + 4 cos(2 x) + 3   cos(3 x) + 3 cos(x)   cos(2 x) + 1
(%o17) ------------------------- + ------------------- + ------------ + cos(x)
                   8                        4                 2
                                                                            + 1
(%i18) 
Run Example
trigexpand(sin(x)/(cos(x)*tan(x)));
                                    sin(x)
(%o1)                            -------------
                                 cos(x) tan(x)
(%i2) 
[acos,atan,diff,sin,sqrt,subst,trigexpand] [atan,subst,tan,trigexpand] [atan,tan,trigexpand] [atan2,collectterms,cos,expand,factor,float,log,plot2d,ratsimp,sin,solve,tan,trigexpand] [block,denom,equal,ev,fullratsimp,lhs,maplist,return,rhs,trigexpand] [coeff,cos,display2d,do,false,makelist,print,ratsubst,sin,sqrt,sum,trigexpand] [coeff,cos,display2d,false,makelist,ratsubst,sin,solve,sqrt,sum,trigexpand] [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,cot,diff,expand,ratsimp,sin,sqrt,subst,trigexpand,trigreduce] [cos,declare,diff,halfangles,pi,radcan,solve,trigexpand,trigrat,trigsimp,true] [cos,diff,integrate,plot2d,trigexpand,trigrat,trigsimp] [cos,diff,sin,trigexpand] [cos,display2d,false,ratsubst,sin,sqrt,sum,trigexpand] [cos,display2d,false,sin,trigexpand,trigreduce,trigsimp] [cos,expand,factor,halfangles,integrate,sin,trigexpand,true] [cos,expand,num,trigexpand,trigsimp] [cos,expand,trigexpand,trigreduce,trigsimp] [cos,factor,rat,ratsubst,sin,trigexpand] [cos,load,sin,sqrt,trigexpand,trigrat,trigreduce,trigsimp] [cos,load,sin,trigexpand,trigsimp] [cos,load,sin,trigexpand] [cos,phi,sum,trigexpand] [cos,pi,sin,trigexpand] [cos,plot2d,rat,ratsubst,sin,trigexpand] [cos,rat,ratsubst,sin,trigexpand] [cos,ratsubst,sin,trigexpand] [cos,sin,subst,trigexpand] [cos,sin,sum,trigexpand] [cos,sin,trigexpand,trigreduce] [cos,sin,trigexpand,trigsimp] [cos,sin,trigexpand,true] [cos,sin,trigexpand] [cos,sqrt,trigexpand,trigsimp] [cos,sqrt,trigexpand] [cos,trigexpand,trigreduce] [cos,trigexpand] [expand,trigexpand] [fullratsimp,load,matrix,radcan,trigexpand,trigsimp] [linsolve,sin,trigexpand] [ratsimp,sin,subst,trigexpand] [sin,sqrt,trigexpand] [sin,subst,trigexpand] [sin,trigexpand,trigreduce,trigsimp] [sin,trigexpand,trigreduce] [sin,trigexpand] [subst,tan,trigexpand] [tan,trigexpand] [trigexpand]

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