# Prove the following

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 :

1. $y(1+x)=1$

2. $x(1+y)=1$

3. $y(1-x)=1$

4. $x(1-y)=1$

Correct Option: , 3

Solution: