### Related

##### trigreduce

trigreduce(sinx+y);

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##### trigreduce

trigreduce(sin3x);

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##### trigreduce

trigreduce(sinx+y);

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##### trigreduce-trigsimp

trigreduce(trigsimp({...

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##### trigreduce

trigreduce((cos^2)*x-...

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##### trigreduce

trigreduce({0,pi/4,pi...

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##### trigreduce

trigreduce((1/(1+tg(%...

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##### trigreduce

trigreduce((cos^2)*x-...

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##### trigreduce

eq1:0.5/(%e^(%i*x)-0.5);

eq2:0.5/(%e^(-%i*x)-0...

eq1*eq2;

Calculate

trigreduce(a);

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### trigreduce

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
```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
```eq3: Lq*cos(x)^2+Ld*sin(x)^2;
2            2
(%o1)                       Ld sin (x) + Lq cos (x)
(%i2) trigsimp(eq3);
2
(%o2)                       (Lq - Ld) cos (x) + Ld
(%i3) trigreduce(eq3);
Lq cos(2 x)   Ld cos(2 x)   Lq   Ld
(%o3)                 ----------- - ----------- + -- + --
2             2        2    2
(%i4) T:matrix([cos(x),sin(x),0],[-sin(x),cos(x),0],[0,0,1]);
[  cos(x)   sin(x)  0 ]
[                     ]
(%o4)                       [ - sin(x)  cos(x)  0 ]
[                     ]
[    0        0     1 ]
(%i5) Tinv:invert(T);
[      cos(x)               sin(x)          ]
[ -----------------  - -----------------  0 ]
[    2         2          2         2       ]
[ sin (x) + cos (x)    sin (x) + cos (x)    ]
[                                           ]
(%o5)            [      sin(x)              cos(x)           ]
[ -----------------   -----------------   0 ]
[    2         2         2         2        ]
[ sin (x) + cos (x)   sin (x) + cos (x)     ]
[                                           ]
[         0                   0           1 ]
(%i6) L:matrix([Lq,0,0],[0,Ld,0],[0,0,Ls]);
[ Lq  0   0  ]
[            ]
(%o6)                           [ 0   Ld  0  ]
[            ]
[ 0   0   Ls ]
(%i7) T*L;
[ Lq cos(x)      0      0  ]
[                          ]
(%o7)                    [     0      Ld cos(x)  0  ]
[                          ]
[     0          0      Ls ]
(%i8) T*L*Tinv;
[          2                               ]
[    Lq cos (x)                            ]
[ -----------------          0          0  ]
[    2         2                           ]
[ sin (x) + cos (x)                        ]
[                                          ]
(%o8)            [                             2            ]
[                       Ld cos (x)         ]
[         0          -----------------  0  ]
[                       2         2        ]
[                    sin (x) + cos (x)     ]
[                                          ]
[         0                  0          Ls ]
(%i9) ```

### Related Help

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