If \( \mathrm{x}=\sum_{\mathrm{n}=0}^{\infty}(-1)^{\mathrm{n}} \tan...

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If \( \mathrm{x}=\sum_{\mathrm{n}=0}^{\infty}(-1)^{\mathrm{n}} \tan ^{2 \mathrm{n}} \theta \) and \( \mathrm{y}=\sum_{\mathrm{n}=0}^{\infty} \cos ^{2 \mathrm{n}} \theta \), for \( 0\theta \)
\( \mathrm{P} \)
WV \( \frac{\pi}{4} \), then:
[JEE Main-2020 (January)]
(1) \( y(1-x)=1 \)
(2) \( y(1+x)=1 \)
(3) \( x(1+y)=1 \)
(4) \( x(1-y)=1 \)
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