Three-Term Inverse Tangent Identity for Product Relation

Three-Term Inverse Tangent Identity for Product Relation

## Formula

If:

$$x+y+z=xyz$$

and the appropriate signs place the sum in the principal interval, then:

$$\tan^{-1}x+\tan^{-1}y+\tan^{-1}z=0$$

or:

$$\pm\pi$$

depending on the signs of $$x,y,z$$.

## Usage

- Used to determine the correct value of sums of three inverse tangent functions using sign analysis.