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## 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  n ln(x), exp(nx) becomes  exp(x)n, sin(2x) becomes  2 sin(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 .
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)

suivant: Combine terms of same monter: Rewriting transcendental and trigonometric précédent: Rewriting transcendental and trigonometric   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse