\(\cot \theta = \frac{x}{y}\) \(\implies \tan \theta = \frac{y}{x}\) \(opp = y; adj = x\) Using Pythagoras theorem, \(Hyp^{2} = Opp^{2} + Adj^{2}\) \(Hyp^{2} = y^{2} + x^{2}\) \(Hyp = \sqrt{y^{2} + x^{2}}\) \(\sin \theta = \frac{y}{\sqrt{y^{2} + x^{2}}}\) \(\therefore \csc \theta = \frac{\sqrt{y^{2} + x^{2}}}{y}\) = \(\frac{1}{y}(\sqrt{y^{2} + x^{2}})\)