1995 AIME Problems/Problem 7

Problem

Given that $\displaystyle (1+\sin t)(1+\cos t)=5/4$ and

$(1-\sin t)(1-\cos t)=\frac mn-\sqrt{k},$

where $\displaystyle k, m,$ and $n$ are positive integers with $\displaystyle m_{}$ and $\displaystyle n_{}$ relatively prime, find $\displaystyle k+m+n.$

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1995 AIME Problems/Problem 7

Problem

Solution

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