Inverse Tangent Sum for Product Greater Than One

Inverse Tangent Sum for Product Greater Than One

## Formula

For $$x,y>0$$ and:

$$xy>1$$

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

## Usage

- Used when the ordinary tangent-addition expression gives a negative principal value but the actual sum lies in the second quadrant.