The title pretty much sums up the question.
If a question has already an accepted answer, should I still try to answer it?
Provided that the answer is not similar to the accepted answer, but an alternative method which may also solve the problem.
Yes, If you think, the new answer will help future visitor, you should. It is encouraged to answer. More option is always better for All.
The answers here are not for the OP only, these are for all the visitors. It is also possible that, the accepted method may not work for some people while, your method is working for them.
And You will find many example of this situation, where a later answer has far many votes than the accepted answer.