If 0<θ<π2 and x=∑n=0∞cos2nθ,y=∑n=0∞sin2nθ,z=∑n=0∞sin2nθ.cos2nθ, then

x=cosec2θ,y=sec2θ,z=11−cos2θ.sin2θ⇒xyz=xy+z

If 0<θ<π2 and x=∑n=0∞cos2nθ,y=∑n=0∞sin2nθ,z=∑n=0∞sin2nθ.cos2nθ, then

x=cosec2θ,y=sec2θ,z=11−cos2θ.sin2θ⇒xyz=xy+z

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If $0 < θ < \frac{π}{2}$ and $x = \sum_{n = 0}^{\infty} \cos^{2 n} θ, y = \sum_{n = 0}^{\infty} \sin^{2 n} θ, z = \sum_{n = 0}^{\infty} \sin^{2 n} θ . \cos^{2 n} θ$ , then

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$x y z = x + y z$

$x y z = x z + y$

$x y z = x y + z$

$x y z = x - y + z$

answer is B.

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$x = \cos e c^{2} θ, y = \sec^{2} θ, z = \frac{1}{1 - \cos^{2} θ . \sin^{2} θ} \Rightarrow x y z = x y + z$

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If 0<θ<π2 and x=∑n=0∞cos2nθ,y=∑n=0∞sin2nθ,z=∑n=0∞sin2nθ.cos2nθ, then

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If $0 < θ < \frac{π}{2}$ and $x = \sum_{n = 0}^{\infty} \cos^{2 n} θ, y = \sum_{n = 0}^{\infty} \sin^{2 n} θ, z = \sum_{n = 0}^{\infty} \sin^{2 n} θ . \cos^{2 n} θ$ , then