1. The problem is to evaluate $\csc^2(45^\circ) - \tan^2(45^\circ)$.\n\n2. Recall the trigonometric identities and values:\n- $\csc(\theta) = \frac{1}{\sin(\theta)}$\n- $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$\n- $\sin(45^\circ) = \cos(45^\circ) = \frac{\sqrt{2}}{2}$\n\n3. Calculate each term:\n- $\csc(45^\circ) = \frac{1}{\sin(45^\circ)} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}$\n- Therefore, $\csc^2(45^\circ) = (\sqrt{2})^2 = 2$\n- $\tan(45^\circ) = 1$\n- Therefore, $\tan^2(45^\circ) = 1^2 = 1$\n\n4. Substitute back into the expression:\n$$\csc^2(45^\circ) - \tan^2(45^\circ) = 2 - 1 = 1$$\n\n5. Final answer: $1$