POSIX Programmer's Manual vs Linux Programmer's Manual

It says that because there's no guarantee that the POSIX manuals (for anything) corresponds to the actual implementation of the corresponding thing on your particular system.

To get the manual for pthread_mutex_trylock(), install the the manual for the library that implements the interface.

On Ubuntu systems, the required manual seems to be part of the glibc-doc package (found by searching for the function name on the Ubuntu package search pages).

The POSIX manual are definitely not useless. The local Linux interface should be compatible with the interface described in the POSIX manual, but the implementation-specific manual may also mentions caveats and Linux-specific implementation details and extensions, and similar non-POSIX functions.

The POSIX manuals becomes extra important if you are concerned about the portability of your code to other Unix systems, in which case you would want to avoid relying on Linux-specific extensions to the POSIX specification.

As of Arch Linux, the package is man-pages from core. Take fcntl for example, after installing man-pages, man 2 fcntl gives the Linux Programmer's Manual page while man 3 fcntl and man fcntl gives the POSIX Programmer's Manual.