{"status": "success", "data": {"description_md": "Given that $(1+\\sin t)(1+\\cos t)=5/4$ and $$ (1-\\sin t)(1-\\cos t)=\\frac mn-\\sqrt{k}, $$ where $k, m,$ and $n$ are positive integers with $m$ and $n$ relatively prime, find $k+m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Given that (1+\\sin t)(1+\\cos t)=5/4 and (1-\\sin t)(1-\\cos t)=\\frac mn-\\sqrt{k}, where k, m, and n are positive integers with m and n relatively prime, find k+m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "1995 AIME Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/95_aime_p08", "prev": "/problem/95_aime_p06"}}