several statements are given regarding trig identities. student is to select which are true and which are false

"}, "advice": "See 12.4, 12.5, 13.4 and the formula sheet.

", "variables": {"statements": {"templateType": "anything", "name": "statements", "group": "do not change these", "description": "", "definition": "map(if(rand[j]=1,\n statements_true[j],\n statements_false[j]),j,0..n-1)"}, "max_mark": {"templateType": "anything", "name": "max_mark", "group": "change these", "description": "", "definition": "6"}, "statements_true": {"templateType": "anything", "name": "statements_true", "group": "change these", "description": "", "definition": "[ \"The formula $\\\\sin(A-B) = \\\\sin(A)\\\\cos(B) - \\\\cos(A)\\\\sin(B)$ is not in the formula sheet\",\n \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is not in the formula sheet\",\n \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is in the formula sheet\",\n \"There are exactly three formulas for $\\\\cos(2A)$ in the formula sheet\",\n \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)+ \\\\frac{1}{2} $\",\n \"$\\\\sin^2(z) = \\\\frac{1}{2} - \\\\frac{1}{2} \\\\cos(2z) $\",\n \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n \"$\\\\cot(\\\\theta) = \\\\frac{1}{\\\\tan(\\\\theta)}$\",\n \"$\\\\sin(-a) = -\\\\sin(a) $\",\n \"$\\\\sin(25) = \\\\sin(20)\\\\cos(5) + \\\\sin(5)\\\\cos(20)$\",\n \"$\\\\tan^2(x) + 1 = \\\\sec^2(x)$\",\n \"$\\\\csc^2(x)=\\\\cot^2(x) + 1$\",\n \"$\\\\cos(A+B)= \\\\cos(A)\\\\cos(B) - \\\\sin(A)\\\\sin(B)$ \" \n]\n "}, "rand": {"templateType": "anything", "name": "rand", "group": "do not change these", "description": "", "definition": "repeat(if(random(0..2)=2,1,0),n)"}, "marks": {"templateType": "anything", "name": "marks", "group": "do not change these", "description": "", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark/3+max_mark/n],[-max_mark/3+max_mark/n,max_mark/n]),j,0..n-1))\n"}, "n": {"templateType": "anything", "name": "n", "group": "change these", "description": "", "definition": "14"}, "statements_false": {"templateType": "anything", "name": "statements_false", "group": "change these", "description": "", "definition": "[ \"The formula $\\\\sin(A-B) = \\\\sin(A)\\\\cos(B) - \\\\cos(A)\\\\sin(B)$ is in the formula sheet\",\n \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is in the formula sheet\",\n \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is not in the formula sheet\",\n \"There are exactly two formulas for $\\\\cos(2A)$ in the formula sheet\",\n \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)- \\\\frac{1}{2} $\",\n \"$\\\\sin^2(z) = \\\\frac{1}{2} \\\\cos(2z) -\\\\frac{1}{2}$\",\n \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n \"$\\\\cot(\\\\theta) = \\\\tan^{-1}(x)$\",\n \"$\\\\sin(-a) = \\\\sin\\\\times (-a) $\",\n \"$\\\\sin(20+5) = \\\\sin(20)\\\\cos(5) + \\\\cos(5)\\\\sin(20)$\",\n \"$\\\\sec^2(x) + 1 = \\\\tan^2(x)$\",\n \"$\\\\cot^2(x) + 1 = \\\\csc^2(t)$\",\n \"$\\\\cos(A+B)= \\\\cos(A)\\\\cos(B) + \\\\sin(A)\\\\sin(B)$ \" \n]"}}, "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n"]}, {"name": "do not change these", "variables": ["rand", "statements", "marks"]}], "tags": [], "parts": [{"maxMarks": "0", "extendBaseMarkingAlgorithm": true, "unitTests": [], "choices": "{statements}", "answers": ["True

", "False

"], "type": "m_n_x", "showCorrectAnswer": true, "warningType": "none", "minMarks": 0, "maxAnswers": 0, "prompt": "Which of the following are true and which are false? If you are unsure of something, find out the answer instead of guessing. A single error will result in a score 0 for the whole question. If you are unable to find out or understand the answer, you are welcome to ask me for help or advice.

\n\nThe formula sheet is in Learning Materials folder in Blackboard.

", "layout": {"type": "all", "expression": ""}, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "showCellAnswerState": true, "shuffleAnswers": false, "shuffleChoices": true, "displayType": "radiogroup", "minAnswers": "{n}", "matrix": "{marks}", "variableReplacementStrategy": "originalfirst", "marks": 0}], "preamble": {"css": "", "js": ""}, "extensions": [], "name": "Algebra. Trigonometric identities. II"}], "pickingStrategy": "all-ordered"}], "contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/", "name": "Lovkush Agarwal"}]}