In the 1998 HSC, question 8 it says 'Prove by induction'. Although there are 2 previous parts to the question, I'm sure Untouchable's proof can be used in the third step...nothing stopping anyone from doing that.
You don't need any special functions for the 4U course. Just the trigonometric functions and addition/subtraction...but I like the Casio fx-100AU, looks better than the fx-82 :p
How about everyone just lays off, yes? Probably more time-productive if one studies non-uniform circular motion instead of arguing about whether one should study it or not.