tan(arcsin(7/8))

{ "query": { "display": "$$\\tan\\left(\\arcsin\\left(\\frac{7}{8}\\right)\\right)$$", "symbolab_question": "TRIG_EVALUATE#\\tan(\\arcsin(\\frac{7}{8}))" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Evaluate Functions", "subTopic": "Simplified", "default": "\\frac{7\\sqrt{15}}{15}", "decimal": "1.80739…", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\tan\\left(\\arcsin\\left(\\frac{7}{8}\\right)\\right)=\\frac{7\\sqrt{15}}{15}$$", "input": "\\tan\\left(\\arcsin\\left(\\frac{7}{8}\\right)\\right)", "steps": [ { "type": "interim", "title": "Rewrite using trig identities:$${\\quad}\\tan\\left(\\arcsin\\left(\\frac{7}{8}\\right)\\right)=\\frac{\\left(\\frac{7}{8}\\right)\\sqrt{1-\\left(\\frac{7}{8}\\right)^{2}}}{1-\\left(\\frac{7}{8}\\right)^{2}}$$", "steps": [ { "type": "step", "primary": "Use the following identity: $$\\tan\\left(\\arcsin\\left(x\\right)\\right)=\\frac{x\\sqrt{1-x^{2}}}{1-x^{2}}$$" }, { "type": "step", "result": "=\\frac{\\left(\\frac{7}{8}\\right)\\sqrt{1-\\left(\\frac{7}{8}\\right)^{2}}}{1-\\left(\\frac{7}{8}\\right)^{2}}" } ], "meta": { "interimType": "Trig Use Identity 1Eq" } }, { "type": "step", "result": "=\\frac{\\frac{7}{8}\\sqrt{1-\\left(\\frac{7}{8}\\right)^{2}}}{1-\\left(\\frac{7}{8}\\right)^{2}}" }, { "type": "step", "primary": "Simplify", "result": "=\\frac{7\\sqrt{15}}{15}" } ], "meta": { "solvingClass": "Trig Evaluate", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions", "practiceTopic": "Evaluate Functions" } }, "meta": { "showVerify": true } }