If $x=\sum_{n=0}^{\infty}(-1)^{n} \tan ^{2 n} \theta$ and $y=\sum_{n=0}^{\infty} \cos ^{2 n} \theta$, for
$0<\theta<\frac{\pi}{4}$, then :
$y(1+x)=1$
$x(1+y)=1$
$y(1-x)=1$
$x(1-y)=1$
Correct Option: , 3
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