To solve the given expression numerically: \[ \frac{1}{1 + \tan^2 \theta} + \frac{1}{1 + \cot^2 \theta} = 1 \] we will evaluate the left-hand side (LHS) for specific values of \(\theta\) and show that it equals the right-hand side (RHS), which is 1. ### Step 1: Recall Trigonometric Identities We know the following trigonometric identities: 1. \(\tan \theta = \frac{\sin \theta}{\cos \theta}\) 2. \(\cot \theta = \frac{\cos \theta}{\sin \theta}\) 3. \(\tan^2 \theta + 1 = \sec^2 \theta\) 4. \(\cot^2 \theta + 1 = \csc^2 \theta\) Using these identities, we can simplify the expression: \[ \frac{1}{1 + \tan^2 \theta} + \frac{1}{1 + \cot^2 \theta} = \cos^2 \theta + \sin^2 \theta = 1 \] Thus, the expression holds true for all values of \(\theta\) where \(\tan