Inverse Sine of a Product

Inverse Sine of a Product

## Formula

For suitable $$x,y$$:

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

provided the sum lies within the principal range.

## Usage

- Used when the sum of two inverse sine terms can be represented by a single inverse sine.