Answer:
A. cos(2x)
Step-by-step explanation:
[tex] \sin \: x( \cos \: x \: \cot \: x - \sin \: x) \\ \\ = \sin \: x \bigg( \cos \: x \times \: \frac{ \cos \: x}{\sin \: x} - \sin \: x \bigg) \\ \\ = \cancel{ \sin \: x} \bigg(\frac{ \cos^{2} \: x - \sin^{2}x}{\cancel{\sin \: x}} \bigg) \\ \\ = \cos^{2} \: x - \sin^{2} x\\ \\ = \cos(2x)[/tex]
