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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