Is it acceptable in an academic interview to pretend like you derived something, or to explaining where it is from Video in reference: https://youtu.be/dUwN6GI-0EQ after 4:05

In a Cambridge (model) interview, someone was asked to sketch a graph of sin(x)/x. The intention was clearly that they were not to have seen this function before. When watching, I immediately recognised this as sinc(x) (a function sometimes used in electrical engineering). They were then told not to evaluate this function at 0 because it's difficult, however I knew how this could be done. If I was in this position, would it be acceptable to pretend like I could derive everything I knew about this function already to impress the interviewer, or important to say that I have already seen the function before.
I really don't think the interviewer cares one way or another whether you've seen the problem before.  She just wants to know if you can solve it, and to hear how you go about it.

In the video, she does say "the function that I'm going to write down, you've probably not seen before"; but I interpret that as just a way to reassure the student that the problem should be possible to solve whether she has seen the function before or not.  It's so the student doesn't panic or get stuck trying to remember the function, rather than actually trying to solve the problem.

So I don't think there is any point in either pretending the problem is new to you, or in announcing that it's familiar.  Neither will significantly help or hurt you in itself.  If you know how to solve the problem, solve it and move on.

On the other hand, it probably wouldn't be helpful to just draw the graph from memory and say "here it is, done".  The interviewer is almost certainly more interested in having you demonstrate that you understand the concepts and methods used to solve the problem, than in seeing if you know the solution.  So you would be wise to work through the problem methodically, explaining what you are doing and how you know to do it.