Inverse Trigonometric Functions

Let $\alpha=3 \sin ^{-1}\left(\frac{6}{11}\right)$ and $\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values.

Given below are two statements :

Statement I : $\quad \cos (\alpha+\beta)>0$.

Statement II : $\quad \cos (\alpha)<0$.

In the light of the above statements, choose the correct answer from the options given below :