ANSWERBy simplifying the left hand side using the Pythagorean Identity.EXPLANATIONThe given identity is [tex] \csc^{2} (x) - \cot^{2} (x) = 1[/tex]Take the left hand side and simplify to get the right hand side.[tex] \csc^{2} (x) - \cot^{2} (x) = \frac{1}{\sin^{2} (x)} - \frac{ \cos^{2} (x)}{\sin^{2} (x)} [/tex]Collect LCM for the denominators.[tex]\csc^{2} (x) - \cot^{2} (x) = \frac{1 - \cos^{2} (x)}{\sin^{2} (x)} [/tex]Recall the Pythagorean Identity.[tex] \cos^{2} (x) + \sin^{2} (x) = 1[/tex]This implies that:[tex]1 - \cos^{2} (x) = \sin^{2} (x)[/tex]We substitute this to get,[tex]\csc^{2} (x) - \cot^{2} (x) = \frac{\sin^{2} (x)}{\sin^{2} (x)} [/tex][tex]\csc^{2} (x) - \cot^{2} (x) = 1[/tex]