What is the simplification of $\frac{\sin^2 x}{(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)}$? What is the simplification of $$\frac{\sin^2 x}{(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)} \space \text{?}$$

What does $1 + \sin^2 x + \sin^4 x + \sin^6 x + ....$ simplify to? 
Or better, what does $1 + x^2 + x^4 + x^6 + ....$ simplify to?
Or better, what does $1 + x + x^2 + x^3 + ....$ simplify to?
