Transforming arccos into arctan: acos2atan

### 5.23.8 Transforming arccos into arctan: acos2atan

The acos2atan command transforms any acoss in an expression to atans, using the identity

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

- acos2atan takes one argument:
  expr, an expression containing inverse trigonometric functions.
- acos2atan(expr) returns expr with any acoss replaced by the appropriate atans.

#### Example

Input:

acos2atan(acos(x))

Output:

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