# Trigonometry! 47

Geometry Level 4

For $0<\phi<\frac {\pi}{2}$, if $x=\displaystyle \sum_{n=0}^{\infty} \cos^{2n} \phi$ $y=\displaystyle \sum_{n=0}^{\infty} \sin^{2n} \phi$ $z=\displaystyle \sum_{n=0}^{\infty} \cos^{2n} \phi \sin^{2n} \phi$ then which of the following holds true?

1. $xyz=xz+y$

2. $xyz=xy+z$

3. $xyz=x+y+z$

4. $xyz=yz+x$

Note that two or three options are correct. Enter the sum of serial numbers of the correct options.

This problem is part of the set Trigonometry.

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