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 $\cot{\theta}$.
$\cot{2\theta} \,=\, \dfrac{\cot^2{\theta}-1}{2\cot{\theta}}$
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.
$(1) \,\,\,\,\,\,$ $\cot{2x} \,=\, \dfrac{\cot^2{x}-1}{2\cot{x}}$
$(2) \,\,\,\,\,\,$ $\cot{2A} \,=\, \dfrac{\cot^2{A}-1}{2\cot{A}}$
$(3) \,\,\,\,\,\,$ $\cot{2\alpha} \,=\, \dfrac{\cot^2{\alpha}-1}{2\cot{\alpha}}$
Learn how to prove the cot double angle identity in trigonometric mathematics by the geometrical approach.
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