### Related

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

trigexpand (p);

Calculate

##### trigexpand

trigexpand((x+3)*(x-3...

Calculate

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

trigexpand(f);

Calculate

##### trigexpand

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

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

trigexpand (p);

Calculate

##### trigexpand

trigexpand(sin3x);

Calculate

##### trigexpand

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

##### trigexpand

trigexpand(sin*(x + y));

Calculate

##### trigexpand

f : ((x+3)*(x-3)-((x+...

trigexpand(f);

Calculate

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

trigexpand (p);

Calculate

### trigexpand

Run Example
```(%i1)trigreduce(trigexpand (sin(3*x)));
3 sin(3 x) + 3 sin(x)   sin(3 x)   3 sin(x)
(%o1)             --------------------- + -------- - --------
4                4          4
(%i2) ```
Run Example
```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) ```

### Related Help

Help for Trigexpand