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 $$\frac{\sin^2 x}{(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)} \space \text{?}$$

Assuming that $x \notin \frac{\pi}{2} + \pi \mathbb{Z}$ you can write $q = \sin^{2}{x}$ with $|q| < 1$ and use the geometric series $\sum_{n=0}^{\infty} q^{n} = \frac{1}{1-q}$.
