Question

(cos2x-sin4x)/sin2x=ctg2x

Answer 1

$frac{cos2x-sin4x}{sin2x} =ctg2x$
$1. frac{cos2x-sin4x}{sin2x}= frac{cos2x}{sin2x}- frac{sin4x}{sin2x}=ctg2x- frac{2sin2x*cos2x}{sin2x}=ctg2x-2cos2x$
$2. ctg2x-2cos2x=ctg2x 2cos2x=0. cos2x=0$
$2x= frac{ pi }{2} + pi n, n$∈Z
$x= frac{ pi }{4} + frac{ pi n}{2} , n$∈Z