glibc defines all of the pthread_* functions weakly within glibc itself so
a program that uses them but does not link with libpthreads will still
function.  The functions are weakly defined to return a "no error" code.

Unfortunately, for some reason pthread_mutex_trylock was left out.

For example, this code works fine whether you link to libpthread or not:
  #include <pthread.h>
  
  int main(int argc,char *argv[])
  {
    pthread_mutex_t mymutex=PTHREAD_MUTEX_INITIALIZER;
  
    pthread_mutex_lock(&mymutex);
  }

On the other hand, this does not work (but should):

  #include <pthread.h>

  int main(int argc,char *argv[])
  {
    pthread_mutex_t mymutex=PTHREAD_MUTEX_INITIALIZER;

    pthread_mutex_trylock(&mymutex);
  }