(cos3x + sin3x)/(cos3x - sin3x) - (cos3x - sin3x)/(cos3x + sin3x) = 2tan6x

help please. I'm lost. I substitute w for 3x then go from there but I get stuck at 4sinwcosw/(2cos^2w-1)

i get stuck at 4sinwcosw/(2cos^2w-1)

2sinwcosw/(cos^2w-sin^2w) is the formula for tan(2w):

tan(2w) = sin(2w)/cos(2w) = 2 sin(w)cos(w)/(2cos(w)-1)

So you're there!