1/(tan(45))

{ "query": { "display": "$$\\frac{1}{\\tan\\left(45^{\\circ\\:}\\right)}$$", "symbolab_question": "TRIG_EVALUATE#\\frac{1}{\\tan(45^{\\circ })}" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{1}{\\tan\\left(45^{\\circ\\:}\\right)}=1$$", "input": "\\frac{1}{\\tan\\left(45^{\\circ\\:}\\right)}", "steps": [ { "type": "interim", "title": "Use the following trivial identity:$${\\quad}\\tan\\left(45^{\\circ\\:}\\right)=1$$", "input": "\\tan\\left(45^{\\circ\\:}\\right)", "steps": [ { "type": "step", "primary": "$$\\tan\\left(x\\right)$$ periodicity table with $$180^{\\circ\\:}n$$ cycle:<br/>$$\\begin{array}{|c|c|}\\hline x&\\tan(x)\\\\\\hline 0&0\\\\\\hline 30^{\\circ }&\\frac{\\sqrt{3}}{3}\\\\\\hline 45^{\\circ }&1\\\\\\hline 60^{\\circ }&\\sqrt{3}\\\\\\hline 90^{\\circ }&\\pm\\infty\\\\\\hline 120^{\\circ }&-\\sqrt{3}\\\\\\hline 135^{\\circ }&-1\\\\\\hline 150^{\\circ }&-\\frac{\\sqrt{3}}{3}\\\\\\hline &\\\\\\hline \\end{array}$$" }, { "type": "step", "result": "=1" } ], "meta": { "interimType": "Trig Trivial Angle Value Title 0Eq" } }, { "type": "step", "result": "=\\frac{1}{1}" }, { "type": "step", "primary": "Simplify", "result": "=1" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }