Inverse Sine of $$\frac{2x}{1+x^2}$$
## Formula
For $$x\in[-1,1]$$:
$$\sin^{-1}\left(\frac{2x}{1+x^2}\right)=2\tan^{-1}x$$
when:
$$2\tan^{-1}x\in\left[-\frac\pi2,\frac\pi2\right]$$
## Usage
- Used to recognize double-angle structures inside inverse sine.