Inverse Sine Difference Formula

Rarely Tested

Inverse Sine Difference Formula

## Formula

$$\sin^{-1}x-\sin^{-1}y=\sin^{-1}\left(x\sqrt{1-y^2}-y\sqrt{1-x^2}\right)$$

provided the resulting principal value lies in the valid range.

## Usage

- Used to simplify the difference of two inverse sine expressions.

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