### 10.2.10 Transforming arcsin into arctan

The asin2atan command transforms arc sines in an expression to arc tangents by using the identity

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

- asin2atan takes expr, an expression containing inverse trigonometric functions.
- asin2atan(expr) returns expr with all instances of asin replaced according to the above formula.

#### Example

asin2atan(asin(x))

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