Trigonometry! 47

Geometry Level 4

For 0<ϕ<π20<\phi<\frac {\pi}{2}, if x=n=0cos2nϕx=\displaystyle \sum_{n=0}^{\infty} \cos^{2n} \phi y=n=0sin2nϕy=\displaystyle \sum_{n=0}^{\infty} \sin^{2n} \phi z=n=0cos2nϕsin2nϕz=\displaystyle \sum_{n=0}^{\infty} \cos^{2n} \phi \sin^{2n} \phi then which of the following holds true?

  1. xyz=xz+yxyz=xz+y

  2. xyz=xy+zxyz=xy+z

  3. xyz=x+y+zxyz=x+y+z

  4. xyz=yz+xxyz=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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