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 :

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true