Let α=3 sin^-1(6/11) and β=3 cos^-1(4/9), where inverse trigonometric functions take only the principal values. Given below are two statements:…

Let $\displaystyle \alpha=3 \sin ^{-1}\left(\frac{6}{11}\right)$ and $\displaystyle \beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values. Given below are two statements : Statement I : $\displaystyle \cos (\alpha+\beta)>0$. Statement II : $\displaystyle \cos (\alpha)<0$. In the light of the above statements, choose the correct answer from the options given below :