In the stability analysis of time-delay systems based on Lyapunov-Krasovskii functionals (LKFs), a core challenge is handling the quadratic terms arising from time-varying delays and ensuring the strict negative definiteness of the resulting derivative matrix. This aspect directly determines the conservatism of the stability conditions formulated as linear matrix inequalities (LMIs). To reduce the conservatism of existing methods, this paper proposes an analytical approach based on delay-interval partitioning and tangent approximation at symmetric points. By dividing the delay interval and introducing tangent constraints at key symmetric points, this method establishes stricter stability criteria, thereby yielding a less conservative set of stability conditions. Results from several typical numerical examples demonstrate that the proposed method achieves lower conservatism compared to existing mainstream approaches.