Transforming arctan into arccos: atan2acos

### 5.23.12 Transforming arctan into arccos: atan2acos

The atan2acos command transforms any atans in an expression to acoss, using the identity

arctan(x) = |
π
2
| − arcsin | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ |
x
√ |
1+x2
| ⎞ ⎟ ⎟ ⎟ ⎟ ⎠

- atan2acos takes one argument:
  expr, an expression containing inverse trigonometric functions.
- atan2acos(expr) returns expr with any atans replaced by the appropriate acoss.

#### Example.

Input:

atan2acos(atan(x))

Output:

π
2
| −arccos | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ |
x
√ |
1+x2
| ⎞ ⎟ ⎟ ⎟ ⎟ ⎠