{ "type": "solutionelement", "name": "solutionelement-checkerdemo", "metadata": {}, "data": { "contents": [{"id": "sdelement-demodata"}], "contentdata": { "sdelement-demodata": { "type": "sdelement", "name": "sdelement-demodata", "metadata": {}, "data": { "dstepdata": { "task-generated-1556533670440-4851": { "readonly": false, "task": [], "assumption": [], "observation": [], "derivmotivation": [], "term": [ { "text": "\\cos\\left(2\\alpha\\right)", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\left(\\cos\\alpha\\right)^2-\\left(\\sin\\alpha\\right)^2", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\left(\\cos\\alpha\\right)^2-\\left(1-\\left(\\cos\\alpha\\right)^2\\right)", "readonly": false, "fillable": false, "attrs": {} }, { "text": "\\left(\\cos\\alpha\\right)^2-1+\\left(\\cos\\alpha\\right)^2", "readonly": false, "fillable": false, "attrs": {} }, { "text": "2\\left(\\cos\\alpha\\right)^2-1", "readonly": false, "fillable": false, "attrs": {} } ], "relation": [ { "text": "=", "readonly": false, "fillable": false, "attrs": {} }, { "text": "=", "readonly": false, "fillable": false, "attrs": {} }, { "text": "=", "readonly": false, "fillable": false, "attrs": {} }, { "text": "=", "readonly": false, "fillable": false, "attrs": {} } ], "motivation": [ { "text": "main double-angle rule for the cosine; $\\cos\\left(2\\alpha\\right)=\\left(\\cos\\alpha\\right)^2-\\left(\\sin\\alpha\\right)^2$", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} }, { "text": "the Pythagorean identity: $\\left(\\cos\\alpha\\right)^2+\\left(\\sin\\alpha\\right)^2=1$", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} }, { "text": "expand the parenthesis", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} }, { "text": "simplify", "readonly": false, "fillable": false, "subshidden": false, "subderiv": [], "attrs": {} } ] } }, "caption": { "text": "Example solution:", "readonly": true, "fillable": false, "attrs": {} }, "dsteps": [ { "id": "task-generated-1556533670440-4851", "type": "task" } ] } } } } }