If , , and , then show xyz = xy +…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

0 < \theta < \frac{\pi}{2}

x = \sum_{n=0}^{\infty} \cos^{2n} \theta

y = \sum_{n=0}^{\infty} \sin^{2n} \theta

and

z = \sum_{n=0}^{\infty} \cos^{2n} \theta \cdot \sin^{2n} \theta

, then show

xyz = xy + z.