### 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

⎞
⎟
⎟
⎟
⎟
⎠