Let \(\alpha =3{\sin }^{-1}\left(\frac{6}{11}\right)\) and \(\beta =3{\cos }^{-1}\left(\frac{4}{9}\right)\), where inver…

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: \(\cos (\alpha +\beta )>0\).
Statement II: \(\cos (\alpha )<0\).
In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2026, 8 Apr (Shift 2)]