Answer:
sec(t)
Step-by-step explanation:
[tex]\frac{cot(t)}{\csc(t)-\sin(t)}}}=\frac{\frac{\cos(t)}{\sin(t)}}{\frac{1}{\sin(t)}-\sin(t)}\\\\[/tex]
[tex]=\frac{\frac{\cos(t)}{\sin(t)}}{\frac{1-\sin^2(t)}{{\sin(t)}}}\\\\=\frac{\cos(t)}{\cos^2(t)}\\\\=\frac{1}{\cos(t)}\\=\sec(t)[/tex]
