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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