Difference between revisions of "1995 AIME Problems/Problem 7"
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== Problem == | == Problem == | ||
Given that <math>\displaystyle (1+\sin t)(1+\cos t)=5/4</math> and | Given that <math>\displaystyle (1+\sin t)(1+\cos t)=5/4</math> and | ||
| − | + | :<math>(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},</math> | |
where <math>\displaystyle k, m,</math> and <math>\displaystyle n_{}</math> are positive integers with <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> relatively prime, find <math>\displaystyle k+m+n.</math> | where <math>\displaystyle k, m,</math> and <math>\displaystyle n_{}</math> are positive integers with <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> relatively prime, find <math>\displaystyle k+m+n.</math> | ||
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== See also == | == See also == | ||
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* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
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| + | {{AIME box|year=1995|num-b=6|num-a=8}} | ||
and
and 
are positive integers with 
and 
