{"status": "success", "data": {"description_md": "If $\\sum\\limits_{n = 0}^{\\infty}\\cos^{2n}\\theta = 5$, what is the value of $\\cos{2\\theta}$?\n\n$\\text {(A) } \\frac15 \\qquad \\text {(B) } \\frac25 \\qquad \\text {(C) } \\frac {\\sqrt5}{5}\\qquad \\text {(D) } \\frac35 \\qquad \\text {(E) }\\frac45$\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>If <span class=\"katex--inline\">\\sum\\limits_{n = 0}^{\\infty}\\cos^{2n}\\theta = 5</span>, what is the value of <span class=\"katex--inline\">\\cos{2\\theta}</span>?</p>&#10;<p><span class=\"katex--inline\">\\text {(A) } \\frac15 \\qquad \\text {(B) } \\frac25 \\qquad \\text {(C) } \\frac {\\sqrt5}{5}\\qquad \\text {(D) } \\frac35 \\qquad \\text {(E) }\\frac45</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2004 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p22", "prev": "/problem/04_amc12A_p20"}}