Mock AIME 1 2007-2008 Problems/Problem 15
Problem
The sum
can be written in the form
, where
are trigonometric functions and
are degrees
. Find
.
Solution
By the product-to-sum identities, we know that , so
:
This sum telescopes (in other words, when we expand the sum, all of the intermediate terms will cancel) to . We now have the desired four terms. There are a couple of ways to express
as primitive trigonometric functions; for example, if we move a
to the denominator, we could express it as
. Either way, we have
, and the answer is
.
See also
Mock AIME 1 2007-2008 (Problems, Source) | ||
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