1995 AIME Problems/Problem 7: Difference between revisions
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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 | ||
<center><math>(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},</math></center> | <center><math>(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},</math></center> | ||
where <math>\displaystyle k, m,</math> and <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> | ||
== Solution == | == Solution == | ||
Revision as of 00:15, 22 January 2007
Problem
Given that 
and
where 
and 
are positive integers with 
and relatively prime, find 
