Transforming arctan into arcsin

### 10.2.11 Transforming arctan into arcsin

The atan2asin command transforms any arc tangents in an expression to arc sines by using the identity

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

- atan2asin takes expr, an expression containing inverse trigonometric functions.
- atan2asin(expr) returns expr with all instances of atan replaced according to the above formula.

#### Example

atan2asin(atan(x))

arcsin | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ |
x
√ |
1+x2
| ⎞ ⎟ ⎟ ⎟ ⎟ ⎠