sin²x + cos²x / 1 - cos²x

Explanation:

Step1: Use trigonometric identity

We know that $\sin^{2}x+\cos^{2}x = 1$ and $1-\cos^{2}x=\sin^{2}x$.

Step2: Substitute identities

Substitute into the given expression: $\frac{\sin^{2}x+\cos^{2}x}{1 - \cos^{2}x}=\frac{1}{\sin^{2}x}=\csc^{2}x$.

Answer:

$\csc^{2}x$