1999 AIME Problems/Problem 11

Problem

Given that $\displaystyle \sum_{k=1}^{35}\sin 5k=\tan \frac mn,$ where angles are measured in degrees, and $\displaystyle m_{}$ and $\displaystyle n_{}$ are relatively prime positive integers that satisfy $\displaystyle \frac mn<90,$ find $\displaystyle m+n.$

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1999 AIME Problems/Problem 11

Problem

Solution

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