### 5.21.1  Expand a transcendental and trigonometric expression : texpand tExpand

texpand or tExpand takes as argument an expression containing transcendental or trigonometric functions.
texpand or tExpand expands these functions, like simultaneous calling expexpand, lnexpand and trigexpand, for example, ln(xn) becomes nln(x), exp(nx) becomes exp(x)n, sin(2x) becomes 2sin(x)cos(x)...
Examples :

1. Expand cos(x+y).
Input :
texpand(cos(x+y))
Output :
cos(x)*cos(y)-sin(x)*sin(y)
2. Expand cos(3x).
Input :
texpand(cos(3*x))
Output :
4*(cos(x))`^` 3-3*cos(x)
3. Expand sin(3*x)+sin(7*x)/sin(5*x).
Input :
texpand((sin(3*x)+sin(7*x))/sin(5*x))
Output
(4*(cos(x))`^`2-1)*(sin(x)/(16*(cos(x))`^`4- 12*(cos(x))`^`2+1))/sin(x)+(64*(cos(x))`^`6- 80*(cos(x))`^`4+24*(cos(x))`^`2-1)*sin(x)/ (16*(cos(x))`^`4-12*(cos(x))`^`2+1)/sin(x)
Output, after a simplification with normal(ans()) :
4*(cos(x))`^`2-2
1. Expand exp(x+y).
Input :
texpand(exp(x+y))
Output :
exp(x)*exp(y)
2. Expand ln(x× y).
Input :
texpand(log(x*y))
Output :
log(x)+log(y)
3. Expand ln(xn).
Input :
texpand(ln(x`^`n))
Output :
n*ln(x)
4. 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+3*2
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 :
cos(x)*cos(y)-sin(x)*sin(y)+exp(x)*exp(y)+ ln(3)+2*ln(x)