Task Efficacy refers a situation when some task produces a specifically desired effect, which is the result of performing the task by human resources who are quite assured of their success in accomplishing the task. For example, designing a website layout is a task that is performed by a web designer to develop a desired design of the website. This task will be efficacious in case the web designer believes in success, so he/she knows how to do the task and has all necessary abilities and tools.
Task efficacy is mainly a theoretical term that comes from the self-efficacy theory. This theory says that a self-efficacious person will do a given task if this person believes in the ability to learn many skills that are required to perform the task. A sense of personal task efficacy serves as the major predictor of success.
Task efficacy and task effectiveness are similar but not equivalent terms. They both determine the ability of some task to produce a desired outcome in the right way. But task efficacy is mostly figured out in bench-tests and lab trials, while task effectiveness is determined and demonstrated in practice.