In the open interval $(1, e)$,\\
I. The function $\sin ( \ln ( x ) )$ is increasing.\\
II. The function $\cos ( \ln ( x ) )$ is increasing.\\
III. The function $\tan ( \ln ( \mathrm { x } ) )$ is increasing.\\
Which of these statements are true?\\
A) Only I\\
B) Only II\\
C) I and III\\
D) II and III\\
E) I, II and III