$\tan{2\theta} \,=\, \dfrac{2\tan{\theta}}{1-\tan^2{\theta}}$
$\dfrac{2\tan{\theta}}{1-\tan^2{\theta}} \,=\, \tan{2\theta}$
It is called tan double angle identity and used as a formula in two cases.
The tangent of double angle identity is used to either expand or simplify the double angle functions like $\tan{2A}$, $\tan{2x}$, $\tan{2\alpha}$ and etc. For example,
$(1) \,\,\,\,\,\,$ $\tan{2x} \,=\, \dfrac{2\tan{x}}{1-\tan^2{x}}$
$(2) \,\,\,\,\,\,$ $\tan{2A} \,=\, \dfrac{2\tan{A}}{1-\tan^2{A}}$
$(3) \,\,\,\,\,\,$ $\tan{2\alpha} \,=\, \dfrac{2\tan{\alpha}}{1-\tan^2{\alpha}}$
Learn how to derive the rule of tan double angle identity by geometric approach in trigonometry.
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