So you maybe know that [tex]\csc x = \frac{1}{\sin x}[/tex]. Now let us try to simplify the expression
[tex]\csc x - \sin x = \frac{1}{\sin x} - \sin x = \frac{1}{\sin x} - \frac{\sin^2 x }{\sin x}=\frac{1-\sin^2 x}{\sin x} = [/tex]
[tex]= \frac{\cos^2 x}{\sin x} = \cot x \cdot \cos x[/tex]
