1. The problem asks if $\sin(76^\circ)$ is equal to $\cos(14^\circ)$.\n\n2. Recall the complementary angle identity in trigonometry: $$\sin(\theta) = \cos(90^\circ - \theta)$$\nThis means the sine of an angle equals the cosine of its complement.\n\n3. Applying this identity to $\sin(76^\circ)$, we get: $$\sin(76^\circ) = \cos(90^\circ - 76^\circ) = \cos(14^\circ)$$\n\n4. Therefore, $\sin(76^\circ)$ is exactly equal to $\cos(14^\circ)$ by the complementary angle rule.\n\nFinal answer: Yes, $\sin(76^\circ) = \cos(14^\circ)$.