Simplify the expression. Write the final form with no fractions. \[ \frac{\sin x}{\sec x \cot x} \] \( \sin ^{2} x \) \( \csc x \) \( \csc ^{2} x \) \( \sin x \)

Step 1: Rewrite the expression \(\frac{\sin x}{\sec x \cot x}\) using trigonometric identities. Recall that \(\sec x = \frac{1}{\cos x}\) and \(\cot x = \frac{\cos x}{\sin x}\). Step 2: Substitute the identities into the expression: \[ \frac{\sin x}{\frac{1}{\cos x} \cdot \frac{\cos x}{\sin x}}. \] Step 3: Simplify the denominator: \[ \frac{\sin x}{\frac{\cos x}{\sin x}} = \frac{\sin x \cdot \sin x}{\cos x} = \frac{\sin^2 x}{\cos x}. \] Step 4: Recognize that \(\frac{\sin^2 x}{\cos x}\) can be rewritten as \(\sin x \cdot \tan x\), but since we need to express it without fractions, we can leave it as is. Step 5: The final simplified form is \(\sin x\).