// Numbas version: finer_feedback_settings
{"name": "Trig identity 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Trig identity 4", "tags": [], "metadata": {"description": "<p>Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Show that the identity \\[(2\\sec\\theta-\\tan\\theta )^2-(\\sec\\theta - 2\\tan\\theta )^2=3\\] is true. Write your proof in your handwritten working.</p>", "advice": "<p>\\begin{align}LHS&amp;=(2\\sec\\theta-\\tan\\theta )^2-(\\sec\\theta - 2\\tan\\theta )^2\\\\&amp;=4\\sec^2\\theta-4\\sec\\theta\\tan\\theta+\\tan^2\\theta-\\left(\\sec^2\\theta-4\\tan\\theta\\sec\\theta+4\\tan^2\\theta\\right)\\\\&amp;=3\\sec^2\\theta-3\\tan^2\\theta\\\\&amp;=3(\\tan^2\\theta+1-\\tan^2\\theta)\\quad\\text{using identity }\\tan^2\\theta+1=\\sec^2\\theta\\\\&amp;=3\\\\&amp;=RHS\\end{align}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}