### 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

⎞
⎟
⎟
⎟
⎟
⎠