Inverse Tangent Sum for Product Less Than One

Inverse Tangent Sum for Product Less Than One

## Formula

If:

$$xy<1$$

and the principal-value condition is satisfied:

$$\tan^{-1}x+\tan^{-1}y=\tan^{-1}\left(\frac{x+y}{1-xy}\right)$$

## Usage

- Used when the denominator $$1-xy$$ is positive and no $$\pi$$ adjustment is required.