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STEP II 2007 question 5 solution
From The Student RoomTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 2007 question 5 solution (i)
(ii) tan is periodic: since
(Cue tedious inductive step, or rather obvious conclusion as (iii) Bit of guesswork involved, but several hints give it away; |t| [U]<[/U] 1, the use of tan in part (ii), and the form of the expression suggest an expression in sin or cos. I chose sin: Let Note also that Then the expression for g can be rewritten as:
And then another small inductive step... let
etc. Hence Solution by generalebriety. |











(or induction if you're bored)
as 3 divides 2007.
, it suffices to prove the result for n = 0, 1, 2 (and then, again, be as fussy as you like about the induction, which I won't).
as required.
as required.
as required.
and
)
so that
so that
Then:






