Find the exact value of the expression. Do not use a calculator. \( \tan 76^{\circ}-\frac{\cos 14^{\circ}}{\cos 76^{\circ}} \) \( \tan 76^{\circ}-\frac{\cos 14^{\circ}}{\cos 76^{\circ}}=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Let's simplify the expression: \[ \tan 76^{\circ} - \frac{\cos 14^{\circ}}{\cos 76^{\circ}} \] **Step 1: Use Co-Function Identities** First, recognize that \(76^{\circ}\) and \(14^{\circ}\) are complementary angles because: \[ 76^{\circ} + 14^{\circ} = 90^{\circ} \] Using the co-function identities: \[ \tan(90^{\circ} - \theta) = \cot \theta \quad \text{and} \quad \cos(90^{\circ} - \theta) = \sin \theta \] So, \[ \tan 76^{\circ} = \tan(90^{\circ} - 14^{\circ}) = \cot 14^{\circ} = \frac{\cos 14^{\circ}}{\sin 14^{\circ}} \] \[ \cos 76^{\circ} = \cos(90^{\circ} - 14^{\circ}) = \sin 14^{\circ} \] **Step 2: Substitute Back into the Expression** Substitute these identities into the original expression: \[ \tan 76^{\circ} - \frac{\cos 14^{\circ}}{\cos 76^{\circ}} = \frac{\cos 14^{\circ}}{\sin 14^{\circ}} - \frac{\cos 14^{\circ}}{\sin 14^{\circ}} \] **Step 3: Simplify** Both terms are identical and thus cancel each other out: \[ \frac{\cos 14^{\circ}}{\sin 14^{\circ}} - \frac{\cos 14^{\circ}}{\sin 14^{\circ}} = 0 \] **Final Answer:** \[ \tan 76^{\circ} - \frac{\cos 14^{\circ}}{\cos 76^{\circ}} = 0 \] **Answer:** \(0\)