2tanx/1+tan²x ekuivalen dengan

[tex] \dfrac{2 \tan x }{1 + \tan^2 x} \\\\\\ = \dfrac{2 \times \frac{\sin x }{\cos x }}{1 + \frac{\sin^2 x}{\cos^2 x }} \\\\\\ = \dfrac{ \frac{2 \sin x}{\cos x}}{ \frac{\cos ^2 x + \sin^2 x}{cos^2 x}} \\\\\\ = \dfrac{ \frac{2 \sin x }{\cos x}}{\frac{1}{\cos^2 x}} \\\\\\ = \dfrac{ 2 \sin x }{\cos x} \times \dfrac{\cos^2 x}{1} \\\\\\ = 2 \sin x \cos x \\ = \sin 2x [/tex]