# Question #b82b5

realize that $1 - {\cos}^{2} x = {\sin}^{2} x$ due to the trigonometric identity ${\sin}^{2} x + {\cos}^{2} x = 1$
therefore the top equation becomes $\sin \left(x\right) \cdot {x}^{2} \cdot \sin \left(x\right)$ which is equal to ${x}^{2} \cdot {\sin}^{2} \left(x\right)$, after removing the common factors ${x}^{2}$ of the denominator and the numerator, you are left with ${\sin}^{2} \frac{x}{x} ^ 4$
the ${\sin}^{2}$ function has its domain over only 1 and 0 so it will never be negative or more than that and the bottom function ${x}^{4}$ gets smaller and smaller as $x$ approaches $0$, so the top function which is a number between 0 and 1 is divided by an increasingly small number, so the limit of the whole function as $x$ approaches 0 is positive Infinity