sin(15)cos(15)+cos(15)sin(15)

{ "query": { "display": "$$\\sin\\left(15^{\\circ\\:}\\right)\\cos\\left(15^{\\circ\\:}\\right)+\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)$$", "symbolab_question": "TRIG_EVALUATE#\\sin(15^{\\circ })\\cos(15^{\\circ })+\\cos(15^{\\circ })\\sin(15^{\\circ })" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\frac{\\sin(\\frac{π}{6})+2\\cos(\\frac{π}{12})\\sin(\\frac{π}{12})}{2}", "decimal": "0.5", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(15^{\\circ\\:}\\right)\\cos\\left(15^{\\circ\\:}\\right)+\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)=\\frac{\\sin\\left(30^{\\circ\\:}\\right)+2\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)}{2}$$", "input": "\\sin\\left(15^{\\circ\\:}\\right)\\cos\\left(15^{\\circ\\:}\\right)+\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)", "steps": [ { "type": "interim", "title": "Rewrite using trig identities:$${\\quad}\\sin\\left(15^{\\circ\\:}\\right)\\cos\\left(15^{\\circ\\:}\\right)=\\frac{\\sin\\left(30^{\\circ\\:}\\right)}{2}$$", "input": "\\sin\\left(15^{\\circ\\:}\\right)\\cos\\left(15^{\\circ\\:}\\right)", "result": "=\\frac{\\sin\\left(30^{\\circ\\:}\\right)}{2}+\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "Use the Double Angle identity: $$2\\sin\\left(x\\right)\\cos\\left(x\\right)=\\sin\\left(2x\\right)$$", "secondary": [ "$$\\sin\\left(x\\right)\\cos\\left(x\\right)=\\frac{\\sin\\left(2x\\right)}{2}$$" ], "result": "=\\frac{\\sin\\left(2\\cdot\\:15^{\\circ\\:}\\right)}{2}" }, { "type": "step", "primary": "Simplify", "result": "=\\frac{\\sin\\left(30^{\\circ\\:}\\right)}{2}" } ], "meta": { "interimType": "Trig Rewrite Using Trig identities Title 0Eq" } }, { "type": "step", "primary": "Simplify", "result": "=\\frac{\\sin\\left(30^{\\circ\\:}\\right)+2\\cos\\left(15^{\\circ\\:}\\right)\\sin\\left(15^{\\circ\\:}\\right)}{2}" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }