If $\alpha =3{\sin }^{-1}\left(\frac{6}{11}\right) and \beta =3{\cos }^{-1}\left(\frac{4}{9}\right),$ where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)

• A

  $\cos \beta >0$
• Correct answer
  B

  $\sin \beta <0$
• Correct answer
  C

  $\cos \left(\alpha +\beta \right)>0$
• Correct answer
  D

  $\cos \alpha <0$

Hence, the correct answer is options: 'B', 'C', 'D'.