$x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta }$ = 1 – tan 2 $\theta$ + tan 2 4$\theta$ + ... = ${1 \over {1 + {{\tan }^2}\theta }}$ = cos 2 $\theta$ ....(1) $y = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta }$ = 1 + cos 2 $\theta$ + cos 4 $\theta$ + cos 6 $\theta$ + .... = ${1 \over {1 - {{\cos }^2}\theta }}$ = ${1 \over {{{\sin }^2}\theta }}$ $\Rightarrow$ sin 2 $\theta$ = ${1 \over y}$ ...(2) Adding (1) and (2), we get, x + ${1 \over y}$ = sin 2 $\theta$ + cos 2 $\theta$ $\Rightarrow$ x + ${1 \over y}$ = 1 $\Rightarrow$ y(1 – x) = 1