\(\csc x = \frac{1}{\sin x}\) Using the quotient rule, \(\frac{\mathrm d y}{\mathrm d x} = \frac{vdu - udv}{v^{2}}\) = \(\frac{\sin x (0) - 1 (\cos x)}{(\sin x)^{2}}\) = \(\frac{- \cos x}{\sin^{2} x}\) = \((\frac{- \cos x}{\sin x}) (\frac{1}{\sin x})\) = \(- \cot x \csc x\)