The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression.
$\frac{\cos^{2} x}{\sin^{2} x} + \csc x \sin x$
$\frac{\cos^{2} x}{\sin^{2} x} + \csc x \sin x =$

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So, the simplified expression is $\csc^{2} x$ .

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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 $\csc^{2} x$ .

The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression.cos2⁡xsin2⁡x+csc⁡xsin⁡xcos2⁡xsin2⁡x+csc⁡xsin⁡x=

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The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression.
$\frac{\cos^{2} x}{\sin^{2} x} + \csc x \sin x$
$\frac{\cos^{2} x}{\sin^{2} x} + \csc x \sin x =$