Expanding transcendental and trigonometric expressions

9.4.1 Expanding transcendental and trigonometric expressions

The texpand or tExpand command expands exponential and trigonometric functions, like simultaneous calling textttexpexpand (see Section 9.3.2), which, for example, expands e^nx as (e^x)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).

texpand takes expr, an expression containing transcendental or trigonometric functions.
texpand(expr) expands these functions.

Examples

Expand cos(x+y).

texpand(cos(x+y))

cosx cosy−sinx siny

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 e^x+y.

texpand(exp(x+y))

e^x e^y

Expand ln(x y).

texpand(log(x*y))

lny+lnx

Expand ln(xⁿ).

texpand(ln(x^n))

n lnx

Expand ln((e²)+e^2ln(2)+e^ln(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)))

Expand e^x+y+cos(x+y)+ln(3x²).

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

cosx cosy−sinx siny+e^x e^y+ln

⎛
⎝

⎞
⎠

+2 ln

⎪
⎪