Trigonometry problem?

ok finally i did it, but it's too long and got too many mistakes in the middle while attempting, is there any easier/simplier way?

LHS:
=((1/tan^2(A)) - 1)sin4A /((1+ cos4A)/tanA)
=(1-tan^2(A))sin4A / tanA(1+cos4A)
=(2tanAsin4A / tan2A) / tanA(1+cos4A)
=2tanAsin4A / tanAtan2A(1+cos4A)
=2sin4A / tan2A(1+cos4A)
=2sin4A / (sin2A(1+cos4A)/cos2A)
=2sin4Acos2A / sin2A(1+cos4A)
= 2(2sin2Acos2A)cos2A / sin2A(1+cos4A)
=4cos^2(2A) / (1+cos4A)
=4cos^2(2A) / (1+2cos^2(2A) -1)
=4cos^2(2A) / 2cos^2(2A)
=2=RHS