$(".my_button").click(function(){

    // if event fired form .trigger() method from other method or event then do something

    // actuall code for click event is here
})

.....
.....

$('.other_first_button').click(function(){
    // code of other first button
    $(".my_button").trigger('click');
});

.....
.....

$('.other_second_button').click(function(){
    // code of other second button
    $(".my_button").trigger('click');
});