The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression.
\[
\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x
\]
\[
\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x=
\]
Answer
So, the simplified expression is \(\boxed{\csc^2 x}\).
Step 1 ：Given the expression \(\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x\)
Step 2 ：We can simplify this using trigonometric identities. The first term is the square of cotangent function, i.e., \(\cot^2 x\). The second term is the product of cosecant and sine function, which simplifies to 1. So, the expression simplifies to \(\cot^2 x + 1\).
Step 3 ：However, we know that \(\cot^2 x + 1 = \csc^2 x\).
Step 4 ：So, the simplified expression is \(\boxed{\csc^2 x}\).
