Solve the equation csc x - sin x = cot x cos x

Work u\sing the left side
Use the reciptional identity: $\csc x=\frac{1}{\sin x}$
$\csc x-\sin x=\frac{1}{\sin x-\sin x}$
Simplify the right side into a \single expression:
$\csc x-\sin x=(1-{\sin }^{2}x)-\sin x$
Use the Pythagorean identity: ${\sin }^{2}x+{\cos }^{2}x=1$
$\csc x-\sin x={\cos }^{2}x\sin x$
Separate as:
$\csc x-\sin x=\frac{\cos x}{\sin x}\times \cos x$
Use the quotient identity: $\cot x=\frac{\cos x}{\sin x}$
$\csc -\sin x=\cot x\cos x$