Given the expression:
[tex]\frac{2\tan18\degree}{1-\tan^218\degree}[/tex]Using the double angle formula for the tangent:
[tex]\tan(2x)=\frac{2\tan x}{1-\tan^2x}[/tex]Finally, we identify x = 18°:
[tex]\frac{2\tan18\degree}{1-\tan^218\degree}=\tan36\degree[/tex]