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

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

It is called cot double angle identity and used as a formula in two cases.

- Cot of double angle is expanded as the quotient of subtraction of one from square of cot function by twice the cot function.
- The quotient of subtraction of one from square of cot function by twice the cot function is simplified as cot of double angle.

The co-tangent of double angle identity is used to either expand or simplify the double angle functions like $\cot{2A}$, $\cot{2x}$, $\cot{2\alpha}$ and etc. For example,

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

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

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

Learn how to derive the rule of cot double angle identity by geometric approach in trigonometry.

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