(3-4cos2A+cos4A)/(3+4cos2A+cos4A)
=(3-4cos2A+2cos^2 2A-1)/(3+4cos2A+2cos^2 2A-1)
=(2cos^2 2A-4cos2A+2)/(2cos^2 2A+4cos2A+2)
=(cos^2 2A-2cos2A+1)/(cos^2 2A+2cos2A+1)
=(cos2A-1)^2/(cos2A+1)^2
=[(1-2sin^2 A)-1]^2/[(2cos^2 A-1)+1]^2
=(4sin^4 A)/(4cos^4 A)
=tan^4 A