Transforming arctan into arcsin: atan2asin

### 5.23.11 Transforming arctan into arcsin: atan2asin

The atan2asin command transforms any atans in an expression to asins, using the identity

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

- atan2asin takes one argument:
  expr, an expression containing inverse trigonometric functions.
- atan2asin(expr) returns expr with any atans replaced by the appropriate asins.

#### Example

Input:

atan2asin(atan(x))

Output:

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