{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"659a13f5-59d1-5b56-813f-e9cabd1ee0f8","task_key":"precalculus--test--659a13f5-59d1-5b56-813f-e9cabd1ee0f8","task_revision_id":"1","upstream_id":"","short_description":"In triangle $ABC,$","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In triangle $ABC,$\\n\\\\[\\\\tan \\\\left( \\\\frac{B - C}{2} \\\\right) \\\\tan \\\\frac{A}{2} = \\\\frac{1}{29} \\\\quad \\\\text{and} \\\\quad \\\\tan \\\\left( \\\\frac{C - A}{2} \\\\right) \\\\tan \\\\frac{B}{2} = \\\\frac{1}{27}.\\\\]Find $\\\\tan \\\\left( \\\\frac{A - B}{2} \\\\right) \\\\tan \\\\frac{C}{2}.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}