{"status": "success", "data": {"description_md": "Find the sum of all the positive solutions of $$2\\cos(2x) \\left(\\cos(2x) - \\cos\\left( \\frac{2014\\pi^2}{x} \\right)\\right) = \\cos(4x) - 1$$\n\n$\\textbf{(A)}\\ \\pi \\qquad\\textbf{(B)}\\ 810\\pi  \\qquad\\textbf{(C)}\\ 1008\\pi \\qquad\\textbf{(D)}\\ 1080 \\pi \\qquad\\textbf{(E)}\\ 1800\\pi$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Find the sum of all the positive solutions of  <span class=\"katex--display\">2\\cos(2x) \\left(\\cos(2x) - \\cos\\left( \\frac{2014\\pi^2}{x} \\right)\\right) = \\cos(4x) - 1</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\pi \\qquad\\textbf{(B)}\\ 810\\pi  \\qquad\\textbf{(C)}\\ 1008\\pi \\qquad\\textbf{(D)}\\ 1080 \\pi \\qquad\\textbf{(E)}\\ 1800\\pi</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2014 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/14_amc12B_p24"}}