### 10.2.12 Transforming arctan into arccos

The atan2acos command transforms any arc tangents in an expression to arc cosines by using the identity

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

- atan2acos takes expr, an expression containing inverse trigonometric functions.
- atan2acos(expr) returns expr with all instances of atan replaced according to the above formula.

#### Example

atan2acos(atan(x))

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