Inverse Sine of $$\frac{2x}{1+x^2}$$

Rarely Tested

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.

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