Expanding transcendental expressions

10.4.1 Expanding transcendental expressions

The texpand or tExpand command expands exponential and trigonometric functions, like simultaneous calling textttexpexpand (see Section 10.3.2), which, for example, expands e^nx as (e^x)ⁿ, lnexpand (see Section 10.3.3), which, for example, expands ln(xⁿ) as nln(x), and trigexpand (see Section 10.2.1), 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))

cos x cos y−sin x sin y

Expand cos(3x).

texpand(cos(3*x))

4 cos ³x−3 cos x

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

texpand((sin(3*x)+sin(7*x))/sin(5*x))

−

2 sin x

⎛
⎝

16 cos ⁴x−12 cos ²x+1

⎞
⎠

sin x

28 sin x cos ²x

⎛
⎝

16 cos ⁴x−12 cos²x+1

⎞
⎠

sin x

−

80 sin x cos ⁴x

⎛
⎝

16 cos ⁴x− 12 cos²x+1

⎞
⎠

sin x

64 sin x cos ⁶x

⎛
⎝

16 cos ⁴x−12 cos ²x+1

⎞
⎠

sin x

normal(ans())

4 cos ²x−2

Expand e^x+y.

texpand(exp(x+y))

e^x e^y

Expand ln(x y).

texpand(log(x*y))

ln y+ln x

Expand ln(xⁿ).

texpand(ln(x^n))

n ln x

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))

cos x cos y−sin x sin y+e^x e^y+ln

⎛
⎝

⎞
⎠

+2 ln

⎪
⎪