Given the expression :
[tex]\cos (\cos ^{-1}(\frac{11}{3}))[/tex]
We should know that : the range of the cosine function is [-1 , 1]
As we can see 11/3 > 1 ,
So, the inverse cosine UNDEFINED
Which mean there is no angle have cosine 11/3
While the expression :
[tex]\tan (\tan ^{-1}(\frac{11}{3}))[/tex]
The expression is DEFINED, because the range of tan function is all the real numbers.
