[tex]sin(2x) = 2 sin x cos x \\ \\ cos(2x) = cos^2 x - sin^2 x[/tex] After Substituting: [tex]\frac{2 sin x cos x}{1+cos^2 x - sin^2 x}[/tex] Use pythagorean thm: [tex]1 - sin^2 x = cos^2 x[/tex] ...................... [tex]\frac{2 sin x cos x}{2cos^2 x} \\ \\ = \frac{sinx }{cos x} \\ \\ = tan x[/tex]
