Principal-Value Rule for $$\tan^{-1}(\tan x)$$

Principal-Value Rule for $$\tan^{-1}(\tan x)$$

## Formula

The value of:

$$\tan^{-1}(\tan x)$$

is the unique angle in:

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

coterminal with $$x$$ modulo $$\pi$$.

## Usage

- Used to correctly simplify inverse tangent of tangent for arbitrary real $$x$$.