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

### 5.23.4 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

  ⎞
  ⎟
  ⎟
  ⎠