Answer
$$\frac{\csc^2 y+\cot^2 y}{\csc^4 y-\cot^4 y}=1$$
The identity is proved to be true.
Work Step by Step
$$\frac{\csc^2 y+\cot^2 y}{\csc^4 y-\cot^4 y}=1$$
First, factoring the denominator on the left side gives $$\frac{\csc^2 y+\cot^2 y}{\csc^4 y-\cot^4 y}$$ $$=\frac{\csc^2 y+\cot^2 y}{(\csc^2 y-\cot^2 y)(\csc^2 y+\cot^2 y)}$$ $$=\frac{1}{\csc^2 y-\cot^2 y}.$$
Now, remember that $\csc^2 y=1+\cot^2 y$, which we would replace as follows $$=\frac{1}{1+\cot^2 y-\cot^2 y}$$ $$=\frac{1}{1}$$ $$=1$$
Hence the identity is proven.
