### 10.2.8 Transforming arccos into arctan

The acos2atan command transforms arc cosines in an expression to arc tangents by using the identity

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

- acos2atan takes expr, an expression containing inverse trigonometric functions.
- acos2atan(expr) returns expr with all instances of acos replaced according to the above formula.

#### Example

acos2atan(acos(x))

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