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

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

## Formula

For $$x\ge0$$:

$$\sin^{-1}\left(\frac{1-x^2}{1+x^2}\right)=\frac\pi2-2\tan^{-1}x$$

when the resulting angle lies in the principal range of $$\sin^{-1}$$.

## Usage

- Used to transform rational expressions involving $$x^2$$ into inverse tangent form.