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9.4.1 Expanding transcendental expressions

The texpand or tExpand command expands exponential and trigonometric functions, like simultaneous calling textttexpexpand (see Section 9.3.2), which, for example, expands enx as (ex)n, lnexpand (see Section 9.3.3), which, for example, expands ln(xn) as nln(x), and trigexpand (see Section 9.2.1), which, for example, expands sin(2x) as 2sin(x)cos(x).

Examples

Expand cos(x+y).

texpand(cos(x+y))
     
cosxcosysinxsiny           

Expand cos(3x).

texpand(cos(3*x))
     
4 cos3x−3 cosx           

Expand sin(3x)+sin(7x)/sin(5x).

texpand((sin(3*x)+sin(7*x))/sin(5*x))
     
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
          
normal(ans())
     
4 cos2x−2           

Expand ex+y.

texpand(exp(x+y))
     
exey           

Expand ln(x y).

texpand(log(x*y))
     
lny+lnx           

Expand ln(xn).

texpand(ln(x^n))
     
nlnx           

Expand ln(e2+e2ln(2)+eln(3)+ln(2)).

texpand(log(e^2)+exp(2*log(2))+exp(log(3)+log(2)))
     
6+2· 3           

or:

texpand(log(e^2)+exp(2*log(2)))+ lncollect(exp(log(3)+log(2)))
     
12           

Expand ex+y+cos(x+y)+ln(3x2).

texpand(exp(x+y)+cos(x+y)+ln(3*x^2))
     
cosxcosysinxsiny+exey+ln
3
+2 ln
x
          

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