Inverse Tangent Difference as a Single Fraction

Inverse Tangent Difference as a Single Fraction

## Formula

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

provided the difference lies within:

$$\left(-\frac\pi2,\frac\pi2\right)$$

## Usage

- Used when the principal-value restriction guarantees that no correction by $$\pi$$ is needed.