Originally Posted by

**grgrsanjay** i don't know weather its grouped correctly(sorry)

for $\displaystyle 0 < \theta < \frac{\pi}{2} $if

$\displaystyle x = \displaystyle\Sigma_{n=0}^{\infty}(\cos ^2n \theta)$

$\displaystyle y = \displaystyle\Sigma_{n=0}^{\infty}(\sin^2n \theta)$

$\displaystyle z = \displaystyle\Sigma_{n=0}^{\infty}(\sin^2n \theta \cos^2n \theta)$

then which of the following are true(multiple choice)

(A)$\displaystyle \frac{1}{x} + \frac{1}{y} = 1$

(B)$\displaystyle x + y +xy =0$

(C)$\displaystyle xyz = xy + z$

(D)$\displaystyle xyz = x + y + z$