# Expand a transcendental and trigonometric expression : texpand tExpand

### 2.20.1 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)`