[tex]\sin x(\cos (x)\cot (x)-\sin (x))[/tex]
Express cot(x) as:
[tex]\begin{gathered} \cot (x)=\frac{\cos (x)}{\sin (x)} \\ so\colon \\ \sin x(\cos (x)\frac{\cos (x)}{\sin (x)}-\sin (x)) \end{gathered}[/tex]
Use distributive property:
[tex]\cos (x)^2-\sin ^2(x)[/tex]
Using the double angle identity:
[tex]\cos ^2(x)-\sin ^2(x)=\cos (2x)[/tex]
Answer:
cos(2x)
