buktikan identitas trigonometri berikut 1- cos4 x/1+ cos 2 x= sin^ x

[tex] \frac{1 - \cos(4x) }{1 + \cos(2x) } = {sin}^{2} x \\ \frac{1 - ( {cos}^{2}2x - {sin}^{2}2x)}{1 + {cos}^{2}x - {sin}^{2}x} \\ \frac{1 - (1 - 2{sin}^{2}2x )}{1 + 1 - 2 {sin}^{2} x} \\ \frac{2 {sin}^{2} 2x}{2(1 - {sin}^{2} x)} \\ \frac{ {(2sin \: x \: cos \: x \: )}^{2} }{ {cos}^{2}x } \\4 {sin}^{2} x[/tex]