### 6.25.1  Expanding transcendental and trigonometric expressions: texpandtExpand

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:  cosx· cosy−sinx· siny
• Expand cos(3x).
Input:
texpand(cos(3*x))
Output:  4 cos3x−3 cosx
• 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()):  4 cos2x−2
• Expand exp(x+y).
Input:
texpand(exp(x+y))
Output:  ex ey
• Expand ln(x× y).
Input:
texpand(log(x*y))
Output:  lny+lnx
• Expand ln(xn).
Input:
texpand(ln(x^n))
Output:  n lnx
• 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:  6+2· 3
or input:
texpand(log(e^2)+exp(2*log(2)))+ lncollect(exp(log(3)+log(2)))
Output:  12
• 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 ⎪ ⎪