tan^2x + cot^2x = 1 -( 2sin^2x + 2sin^4x) / (sin^2x - sin^4x)
tan^2x = sin^2x/cos^2x , cot^2x = cos^2x/sin^2x
sin^2x/cos^2x + cos^2x/sin^2 =
(sin^4x+cos^4x)/sin^2x*cos^2x =
((sin^4x+(1-sin^2x)^2)/(sin^2x(1-sin^2x))=
((sin^4x+1-2sin^2x+sin^4x))/(sin^2x-sin^4x)=
(1-2sin^2x+2sin^4x)/(sin^2x - sin^4x)
It is right