6.25.1 Expanding transcendental and trigonometric expressions: texpand tExpand
The texpand command expands exponential
and trigonometric functions, like simultaneous calling:
expexpand (see Section 6.24.2), which, for example,
expands exp(nx) as exp(x)n,
lnexpand (see Section 6.24.3), which, for example,
expands ln(xn) as nln(x) , and
trigexpand (see Section 6.23.1), which, for
example, expands sin(2x) as 2sin(x)cos(x).
tExpand is a synonym for texpand.
-
texpand takes one argument:
expr, an expression containing transcendental or trigonometric functions.
- texpand(expr) expands these functions.
Examples.
-
Expand cos(x+y).
Input:
texpand(cos(x+y))
Output:
- Expand cos(3x).
Input:
texpand(cos(3*x))
Output:
- Expand sin(3*x)+sin(7*x)/sin(5*x).
Input:
texpand((sin(3*x)+sin(7*x))/sin(5*x))
Output:
| − | 2 sinx |
|
⎛
⎝ | 16 cos4x−12 cos2x+1 | ⎞
⎠ | sinx |
|
| +
| 28 sinx· cos2x |
|
⎛
⎝ | 16 cos4x−12
cos2x+1 | ⎞
⎠ | sinx |
|
| − |
| |
| 80 sinx· cos4x |
|
⎛
⎝ | 16 cos4x−
12 cos2x+1 | ⎞
⎠ | sinx |
|
| + | 64 sinx· cos6x |
|
⎛
⎝ | 16 cos4x−12 cos2x+1 | ⎞
⎠ | sinx |
|
|
| |
|
Output, after a simplification with normal(ans()):
- Expand exp(x+y).
Input:
texpand(exp(x+y))
Output:
- Expand ln(x× y).
Input:
texpand(log(x*y))
Output:
- Expand ln(xn).
Input:
texpand(ln(x^n))
Output:
- Expand ln((e2)+exp(2*ln(2))+exp(ln(3)+ln(2))).
Input:
texpand(log(e^2)+exp(2*log(2))+exp(log(3)+log(2)))
Output:
or input:
texpand(log(e^2)+exp(2*log(2)))+ lncollect(exp(log(3)+log(2)))
Output:
- Expand exp(x+y)+cos(x+y)+ln(3x2).
Input:
texpand(exp(x+y)+cos(x+y)+ln(3*x^2))
Output:
cosx· cosy−sinx· siny+ex ey+ln | ⎛
⎝ | 3 | ⎞
⎠ | +2 ln | ⎪
⎪ | x | ⎪
⎪ |