For 0<ϕ<π/2, if x=∑n=0∞ cos2n⁡ϕ,y=∑n=0∞ sin2n⁡ϕ  ,z=∑n=0∞ cos2n⁡ϕsin2n⁡ϕ, then

All are infinite geometric progression with common ratio < Ix=11−cos2⁡ϕ=1sin2⁡ϕ,y=11−sin2⁡ϕ=1cos2⁡ϕ,z=11−cos2⁡ϕsin2⁡ϕnow, xy+z=1sin2⁡ϕcos2⁡ϕ+11−sin2⁡ϕcos2⁡ϕ =1sin2⁡ϕcos2⁡ϕ1−sin2⁡ϕcos2⁡ϕxy+z=xyz-----------(i)clearly, x+y=sin2⁡ϕ+cos2⁡ϕsin2⁡ϕcos⁡ϕ=xyx+y+z=xyz    [using Eq. (i)]