If $ x=\sum_{n=0}^{\infty}(-1)^{n} \tan ^{2 n} \theta $ and $ y=\sum_{n=0}^{\infty} \cos ^{2 n} \theta $ for $ 0

Question

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

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If \( x=\sum_{n=0}^{\infty}(-1)^{n} \tan ^{2 n} \theta \) and \( y=\sum_{n=0}^{\infty} \cos ^{2 n} \theta \) for \( 0&lt…