6.23.4  Putting together sine and cosine of the same angle: tcollect tCollect

The tcollect command linearizes trigonometric expressions (in terms of sin(n*x) and cos(n*x)) and combines sines and cosines of the same angle.
tCollect is a synonym for tcollect.

• tcollect takes one argument:
  expr, an expression containing trigonometric functions.
• tcollect(expr) returns expr after first linearizing it and then combining sines and cosines of the same angle.

Examples.

• Input:
  tcollect(sin(x)+cos(x))
  Output:

  √

  2

  cos

  ⎛ ⎜ ⎜ ⎝

  x−

  1 4

  π

  ⎞ ⎟ ⎟ ⎠

• Input:
  tcollect(2*sin(x)*cos(x)+cos(2*x))
  Output:

  √

  2

  cos

  ⎛ ⎜ ⎜ ⎝

  2 x−

  1 4

  π

  ⎞ ⎟ ⎟ ⎠