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In this paper, we study the regularity of the Lyapunov exponent forquasiperiodic Schr\"odinger cocycles with $C^2$ cos-type potentials, largecoupling constants, and a fixed Diophantine frequency. We obtain the absolutecontinuity of the Lyapunov exponent. Moreover, we prove the Lyapunov exponentis $\frac{1}{2}$-H\"older continuous and a better regularity cannot beexpected. Furthermore, for any given $r\in (\frac12, 1)$, we can find someenergy in the spectrum where the local regularity of the Lyapunov exponent isbetween $(r-\epsilon)$-H\"older continuity and $(r+\epsilon)$-H\"oldercontinuity.

The precise regularity of the Lyapunov exponent for Cos-type quasiperiodic Schr\"odinger cocycles with large couplings