1) Write the expression in terms of sine and cosine, then simplify : \( \sin x \cot x= \) a) \( \frac{\sin ^{2} x}{\cos x} \) b) \( \sin x \cos x \) c) \( \cos x \) d) \( \tan x \)

To simplify the expression \( \sin x \cot x \), we start by recalling the definition of cotangent: \[ \cot x = \frac{\cos x}{\sin x} \] Now, substituting this definition into the expression: \[ \sin x \cot x = \sin x \cdot \frac{\cos x}{\sin x} \] The \( \sin x \) in the numerator and denominator cancels out (assuming \( \sin x \neq 0 \)): \[ \sin x \cot x = \cos x \] Thus, the simplified expression is: \[ \sin x \cot x = \cos x \] The correct answer is: c) \( \cos x \)