6.25.1  Expanding transcendental and trigonometric expressions: texpand tExpand

The texpand command expands exponential and trigonometric functions, like simultaneous calling:
expexpand (see Section 6.24.2), which, for example, expands exp(nx) as exp(x)ⁿ,
lnexpand (see Section 6.24.3), which, for example, expands ln(xⁿ) as nln(x) , and
trigexpand (see Section 6.23.1), which, for example, expands sin(2x) as 2sin(x)cos(x).
tExpand is a synonym for texpand.

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

Examples.

• Expand cos(x+y).
  Input:
  texpand(cos(x+y))
  Output:

  cosx· cosy−sinx· siny

• Expand cos(3x).
  Input:
  texpand(cos(3*x))
  Output:

  4 cos3x−3 cosx

• Expand sin(3*x)+sin(7*x)/sin(5*x).
  Input:
  texpand((sin(3*x)+sin(7*x))/sin(5*x))
  Output:

  − 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

  Output, after a simplification with normal(ans()):

  4 cos2x−2

• Expand exp(x+y).
  Input:
  texpand(exp(x+y))
  Output:

  ex ey

• Expand ln(x× y).
  Input:
  texpand(log(x*y))
  Output:

  lny+lnx

• Expand ln(xⁿ).
  Input:
  texpand(ln(x^n))
  Output:

  n lnx

• 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+2· 3

  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:

  cosx· cosy−sinx· siny+ex ey+ln

  ⎛ ⎝

  3

  ⎞ ⎠

  +2 ln

  ⎪ ⎪

  x

  ⎪ ⎪