# Cot double angle formula

The expansion of cotangent of double angle in terms of cot of angle is called cot double angle identity and it is used as a formula to expand cot functions that contains double angle in terms of cot of angle.

If theta is an angle, then cot double angle function is $\cot{2\theta}$ and the expansion of cot double angle formula is in terms of $\cot{\theta}$.

## Formula

$\cot{2\theta} \,=\, \dfrac{\cot^2{\theta}-1}{2\cot{\theta}}$

### Other form

Angle can be represented by any symbol but the expansion of cot double angle formula is always in the same form. $\cot{2x}$, $\cot{2A}$ and $\cot{2\alpha}$ are some of the most common representations of cot double angle identity in trigonometric mathematics.

$(1) \,\,\,\,\,\,$ $\cot{2x} \,=\, \dfrac{\cot^2{x}-1}{2\cot{x}}$

$(2) \,\,\,\,\,\,$ $\cot{2A} \,=\, \dfrac{\cot^2{A}-1}{2\cot{A}}$

$(3) \,\,\,\,\,\,$ $\cot{2\alpha} \,=\, \dfrac{\cot^2{\alpha}-1}{2\cot{\alpha}}$

#### Proof

Learn how to prove the cot double angle identity in trigonometric mathematics by the geometrical approach.