sin(2x-20)=-cos(3x+50)

{ "query": { "display": "$$\\sin\\left(2x-20\\right)=-\\cos\\left(3x+50\\right)$$", "symbolab_question": "EQUATION#\\sin(2x-20)=-\\cos(3x+50)" }, "solution": { "level": "PERFORMED", "subject": "Trigonometry", "topic": "Trig Equations", "subTopic": "Trig Equations", "default": "x=2πn+\\frac{π}{2}-70,x=-\\frac{4πn+60+π}{10}", "degrees": "x=-3920.70456…^{\\circ }+360^{\\circ }n,x=-361.77467…^{\\circ }-72^{\\circ }n", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\sin\\left(2x-20\\right)=-\\cos\\left(3x+50\\right){\\quad:\\quad}x=2πn+\\frac{π}{2}-70,\\:x=-\\frac{4πn+60+π}{10}$$", "input": "\\sin\\left(2x-20\\right)=-\\cos\\left(3x+50\\right)", "steps": [ { "type": "step", "primary": "Multiply by $$-1$$", "result": "-\\sin\\left(2x-20\\right)=\\cos\\left(3x+50\\right)" }, { "type": "interim", "title": "Rewrite using trig identities", "input": "-\\sin\\left(2x-20\\right)=\\cos\\left(3x+50\\right)", "result": "\\sin\\left(-\\left(2x-20\\right)\\right)=\\sin\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)", "steps": [ { "type": "step", "primary": "Use the following identity: $$-\\sin\\left(x\\right)=\\sin\\left(-x\\right)$$", "result": "\\sin\\left(-\\left(2x-20\\right)\\right)=\\cos\\left(3x+50\\right)" }, { "type": "step", "primary": "Use the following identity: $$\\cos\\left(x\\right)=\\sin\\left(\\frac{π}{2}-x\\right)$$", "result": "\\sin\\left(-\\left(2x-20\\right)\\right)=\\sin\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)" } ], "meta": { "interimType": "Trig Rewrite Using Trig identities 0Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7SHDS6kJwJIV4q/3HJvK1hgojcsWaAj7I4KDJZ+q/zjaH0xHbffF9yQV56c+XOmsUEsLZPw0Vm9MD6l9/kB1c91f2VE3iaVir/MjR2DERcZ0+92eGLSzeVn4MnusSJN6pU9xzI0Qe+kmlPzCUw2pJ5x6r1lQlCQUbUfH+IeviT/r4rA4RYMYJMwO6oSEMR1mNo3oe/oyhMy2+1TQhDBd2fwFKHQ6RGVQjiWOq5H13FZKmjkCCyn9Od0fQyCWmlpOzHOrX7UzWNirFLb1W4rOczQ==" } }, { "type": "interim", "title": "Apply trig inverse properties", "input": "\\sin\\left(-\\left(2x-20\\right)\\right)=\\sin\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)", "result": "-\\left(2x-20\\right)=\\frac{π}{2}-\\left(3x+50\\right)+2πn,\\:-\\left(2x-20\\right)=π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn", "steps": [ { "type": "step", "primary": "$$\\sin\\left(x\\right)=\\sin\\left(y\\right)\\quad\\Rightarrow\\quad\\:x=y+2{\\pi}n,\\:x=\\pi-y+2{\\pi}n$$", "result": "-\\left(2x-20\\right)=\\frac{π}{2}-\\left(3x+50\\right)+2πn,\\:-\\left(2x-20\\right)=π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn" } ], "meta": { "interimType": "Trig Apply Inverse Props 0Eq" } }, { "type": "interim", "title": "$$-\\left(2x-20\\right)=\\frac{π}{2}-\\left(3x+50\\right)+2πn{\\quad:\\quad}x=2πn+\\frac{π}{2}-70$$", "input": "-\\left(2x-20\\right)=\\frac{π}{2}-\\left(3x+50\\right)+2πn", "steps": [ { "type": "interim", "title": "Expand $$-\\left(2x-20\\right):{\\quad}-2x+20$$", "input": "-\\left(2x-20\\right)", "steps": [ { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(2x\\right)-\\left(-20\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$-\\left(-a\\right)=a,\\:\\:\\:-\\left(a\\right)=-a$$" ], "result": "=-2x+20" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ZZm6vZxAa9bil1RzD0KR+Qy/iZ4ehKY+CVw1ErkP2bsF0f9e9MOLJfBD6LX95TzkeFr9fJWrn4Z0QR9jTkKwM0DLjX7DcYtB54q3geRNejHEepKFwrkBZOTElTVsJWGVvzIPeEtDfcHv/z8uls8Teg==" } }, { "type": "interim", "title": "Expand $$\\frac{π}{2}-\\left(3x+50\\right)+2πn:{\\quad}\\frac{π}{2}-3x-50+2πn$$", "input": "\\frac{π}{2}-\\left(3x+50\\right)+2πn", "steps": [ { "type": "interim", "title": "$$-\\left(3x+50\\right):{\\quad}-3x-50$$", "input": "-\\left(3x+50\\right)", "result": "=\\frac{π}{2}-3x-50+2πn", "steps": [ { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(3x\\right)-\\left(50\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$+\\left(-a\\right)=-a$$" ], "result": "=-3x-50" } ], "meta": { "interimType": "N/A" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYn9eF/2A+xeBD8zmPv7S5luIydchH6mcwpw4uJvqv2+PdQxShwOg3W+URNAMu5sPa6VYwrogLl29RT6HYd2NJ316pfF1z6umzUJTJvt+ojYZEgMzQ6KqRUeJ0bFe7kX7pQINwg5QmdsTgMIvElTdl0sceFyf+uA6Q2Ysf1eSxiTL" } }, { "type": "step", "result": "-2x+20=\\frac{π}{2}-3x-50+2πn" }, { "type": "interim", "title": "Move $$20\\:$$to the right side", "input": "-2x+20=\\frac{π}{2}-3x-50+2πn", "result": "-2x=-3x+2πn+\\frac{π}{2}-70", "steps": [ { "type": "step", "primary": "Subtract $$20$$ from both sides", "result": "-2x+20-20=\\frac{π}{2}-3x-50+2πn-20" }, { "type": "interim", "title": "Simplify", "input": "-2x+20-20=\\frac{π}{2}-3x-50+2πn-20", "result": "-2x=-3x+2πn+\\frac{π}{2}-70", "steps": [ { "type": "interim", "title": "Simplify $$-2x+20-20:{\\quad}-2x$$", "input": "-2x+20-20", "steps": [ { "type": "step", "primary": "Add similar elements: $$20-20=0$$" }, { "type": "step", "result": "=-2x" } ], "meta": { "interimType": "Generic Simplify Specific 1Eq" } }, { "type": "interim", "title": "Simplify $$\\frac{π}{2}-3x-50+2πn-20:{\\quad}-3x+2πn+\\frac{π}{2}-70$$", "input": "\\frac{π}{2}-3x-50+2πn-20", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=-3x+2πn+\\frac{π}{2}-50-20" }, { "type": "step", "primary": "Subtract the numbers: $$-50-20=-70$$", "result": "=-3x+2πn+\\frac{π}{2}-70" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": 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"-2x+3x=-3x+2πn+\\frac{π}{2}-70+3x" }, { "type": "step", "primary": "Simplify", "result": "x=2πn+\\frac{π}{2}-70" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "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" } } ], "meta": { "solvingClass": "Equations", "interimType": "Equations" } }, { "type": "interim", "title": "$$-\\left(2x-20\\right)=π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn{\\quad:\\quad}x=-\\frac{4πn+60+π}{10}$$", "input": "-\\left(2x-20\\right)=π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn", "steps": [ { "type": "interim", "title": "Expand $$-\\left(2x-20\\right):{\\quad}-2x+20$$", "input": "-\\left(2x-20\\right)", "steps": [ { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(2x\\right)-\\left(-20\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$-\\left(-a\\right)=a,\\:\\:\\:-\\left(a\\right)=-a$$" ], "result": "=-2x+20" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7ZZm6vZxAa9bil1RzD0KR+Qy/iZ4ehKY+CVw1ErkP2bsF0f9e9MOLJfBD6LX95TzkeFr9fJWrn4Z0QR9jTkKwM0DLjX7DcYtB54q3geRNejHEepKFwrkBZOTElTVsJWGVvzIPeEtDfcHv/z8uls8Teg==" } }, { "type": "interim", "title": "Expand $$π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn:{\\quad}π-\\frac{π}{2}+3x+50+2πn$$", "input": "π-\\left(\\frac{π}{2}-\\left(3x+50\\right)\\right)+2πn", "steps": [ { "type": "interim", "title": "$$-\\left(3x+50\\right):{\\quad}-3x-50$$", "input": "-\\left(3x+50\\right)", "steps": [ { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(3x\\right)-\\left(50\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$+\\left(-a\\right)=-a$$" ], "result": "=-3x-50" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=π-\\left(-3x+\\frac{π}{2}-50\\right)+2πn" }, { "type": "interim", "title": "$$-\\left(\\frac{π}{2}-3x-50\\right):{\\quad}-\\frac{π}{2}+3x+50$$", "input": "-\\left(\\frac{π}{2}-3x-50\\right)", "result": "=π-\\frac{π}{2}+3x+50+2πn", "steps": [ { "type": "step", "primary": "Distribute parentheses", "result": "=-\\left(\\frac{π}{2}\\right)-\\left(-3x\\right)-\\left(-50\\right)" }, { "type": "step", "primary": "Apply minus-plus rules", "secondary": [ "$$-\\left(-a\\right)=a,\\:\\:\\:-\\left(a\\right)=-a$$" ], "result": "=-\\frac{π}{2}+3x+50" } ], "meta": { "interimType": "N/A" } } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Expand Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7y8RdtQbqcqkCTkMN3ZLu8ynBAktAb3E/vJyoPMn4Y2Td5gzzYiNtvFQz080VikXzm8Cy3/+KhUDPMF7zx3LrTDrItGTK5senSF/kdAFuKtRFKk3fejFkyiOiq9iG9IkAg+TSL+/6ntLOpwwfva9DT9BBED7eEz/5dwfOroArw2V0ZtI1KnPgvxgQrSLoAYVy" } }, { "type": "step", "result": "-2x+20=π-\\frac{π}{2}+3x+50+2πn" }, { "type": "interim", "title": "Move $$20\\:$$to the right side", "input": "-2x+20=π-\\frac{π}{2}+3x+50+2πn", "result": "-2x=3x+2πn+30+π-\\frac{π}{2}", "steps": [ { "type": "step", "primary": "Subtract $$20$$ from both sides", "result": "-2x+20-20=π-\\frac{π}{2}+3x+50+2πn-20" }, { "type": "interim", "title": "Simplify", "input": "-2x+20-20=π-\\frac{π}{2}+3x+50+2πn-20", "result": "-2x=3x+2πn+30+π-\\frac{π}{2}", "steps": [ { "type": "interim", "title": "Simplify $$-2x+20-20:{\\quad}-2x$$", "input": "-2x+20-20", "steps": [ { "type": "step", "primary": "Add similar elements: $$20-20=0$$" }, { "type": "step", "result": "=-2x" } ], "meta": { "interimType": "Generic Simplify Specific 1Eq" } }, { "type": "interim", "title": "Simplify $$π-\\frac{π}{2}+3x+50+2πn-20:{\\quad}3x+2πn+30+π-\\frac{π}{2}$$", "input": "π-\\frac{π}{2}+3x+50+2πn-20", "steps": [ { "type": "step", "primary": "Group like terms", "result": "=3x+π+2πn-\\frac{π}{2}+50-20" }, { "type": "step", "primary": "Add/Subtract the numbers: $$50-20=30$$", "result": "=3x+2πn+30+π-\\frac{π}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": 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"-2x-3x=3x+2πn+30+π-\\frac{π}{2}-3x" }, { "type": "step", "primary": "Simplify", "result": "-5x=2πn+30+π-\\frac{π}{2}" } ], "meta": { "interimType": "Move to the Left Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7RluGULp3PbeHYAm8DpBGfPUK0Bf149Kyagz806f4PTVY6bwfxsFXqNfqyezH8YiYSDj4+97zAezt9PwT9bHGu69Equxs5h2+pg6Zx58ufQKAqomnF50Zs2t8jA+QD47lMqZoVC7f1Q8ujn0uIpGrSiSIB+5rZzjN9rZB584s2S28VmH5b+IMwMCjiIIju0VR3CmpoWEZ6Xx6oiIfKYR080iu613x5IyBSj4elHIXAAwF+/jU5cejOvmDrkqvguX1zFCnzKTYR2+JO9+HPqu47+jt0hWgBMP6WmJL3zDfowuIejL9cTIvq532d8wlmk5jjc4uAgN5eg1K/8JxeGgebgXXSkuG634JZ0lja1+WrR3WmK64en8Tg8KsMmLPqU8u4bsSxBVtCKzG8EljRiQ7YwXXSkuG634JZ0lja1+WrR12yJZbv9JNC1KQm2KBNDOOTgtV8UeTlOjbrwiqNnnwotJhpA9/uD9yR/Ph6qaWFfU5KyHsrQ3tO6RK1e6/Vd+sla1GEiD7QoTLIeMLN4jcH9BqKkduvWeZ1aldjNufzcHKzgkJ9epXAVEg8k0yhQGHethhpyrQTda4SvUcZm/KsO/Ab3cSzX/gB4rYp7EKXevaWePPEqfUesyCUnC0AMtrqiWfjnO2oiny8qhYyTA7lfBgeR+YcdPN7cleTcuOImk=" } }, { "type": "interim", "title": "Divide both sides by $$-5$$", "input": "-5x=2πn+30+π-\\frac{π}{2}", "result": "x=-\\frac{4πn+60+π}{10}", "steps": [ { "type": "step", "primary": "Divide both sides by $$-5$$", "result": "\\frac{-5x}{-5}=\\frac{2πn}{-5}+\\frac{30}{-5}+\\frac{π}{-5}-\\frac{\\frac{π}{2}}{-5}" }, { "type": "interim", "title": "Simplify", "input": "\\frac{-5x}{-5}=\\frac{2πn}{-5}+\\frac{30}{-5}+\\frac{π}{-5}-\\frac{\\frac{π}{2}}{-5}", "result": "x=-\\frac{4πn+60+π}{10}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{-5x}{-5}:{\\quad}x$$", "input": "\\frac{-5x}{-5}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{-a}{-b}=\\frac{a}{b}$$", "result": "=\\frac{5x}{5}" }, { "type": "step", "primary": "Divide the numbers: $$\\frac{5}{5}=1$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7YoJhQWmEu9VNJo28CPisH3yRHuGw7+tM5METTDj6vVEed1oZgJr3Rrt+25B4RF18ZEt3ZXAiqUE0HIXrrrezJHZKl2mV4AlztiApTAFigz0dWZAkmURnuRS8qK/QQHXTialcV/dI5TH4fXyp+ncwuA==" } }, { "type": "interim", "title": "Simplify $$\\frac{2πn}{-5}+\\frac{30}{-5}+\\frac{π}{-5}-\\frac{\\frac{π}{2}}{-5}:{\\quad}-\\frac{4πn+60+π}{10}$$", "input": "\\frac{2πn}{-5}+\\frac{30}{-5}+\\frac{π}{-5}-\\frac{\\frac{π}{2}}{-5}", "steps": [ { "type": "step", "primary": "Apply rule $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{2πn+30+π-\\frac{π}{2}}{-5}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{-b}=-\\frac{a}{b}$$", "result": "=-\\frac{2πn+30+π-\\frac{π}{2}}{5}" }, { "type": "interim", "title": "Join $$2πn+30+π-\\frac{π}{2}:{\\quad}\\frac{4πn+60+π}{2}$$", "input": "2πn+30+π-\\frac{π}{2}", "result": "=-\\frac{\\frac{4πn+π+60}{2}}{5}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$2πn=\\frac{2πn2}{2},\\:30=\\frac{30\\cdot\\:2}{2},\\:π=\\frac{π2}{2}$$", "result": "=\\frac{2πn\\cdot\\:2}{2}+\\frac{30\\cdot\\:2}{2}+\\frac{π2}{2}-\\frac{π}{2}" }, { "type": "step", "primary": "Since the denominators are equal, combine the fractions: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{2πn\\cdot\\:2+30\\cdot\\:2+π2-π}{2}" }, { "type": "interim", "title": "$$2πn\\cdot\\:2+30\\cdot\\:2+π2-π=4πn+60+π$$", "input": "2πn\\cdot\\:2+30\\cdot\\:2+π2-π", "steps": [ { "type": "step", "primary": "Add similar elements: $$2π-π=π$$", "result": "=2\\cdot\\:2πn+30\\cdot\\:2+π" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2=4$$", "result": "=4πn+30\\cdot\\:2+π" }, { "type": "step", "primary": "Multiply the numbers: $$30\\cdot\\:2=60$$", "result": "=4πn+60+π" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s722rs/UtTzhh0/11VX7Cb4za0QEVIYcJLdlK0K9gYhcoAlilG71elit3w1IBbYN0Ps5Hw/UF82SQGVYL13IS1/57uIz3Z8/mqbWPHAPICx4ePCZX1LCCWZV5U81JkKqM1KUH6sOnLYua+pSwvkC9idOpmOjaNI0KtlNPxhy2Xu2KwiNrEngO+NNvZ9sqNu+2V" } }, { "type": "step", "result": "=\\frac{4πn+60+π}{2}" } ], "meta": { "interimType": "Algebraic Manipulation Join Concise Title 1Eq" } }, { "type": "interim", "title": "Simplify $$\\frac{\\frac{4πn+60+π}{2}}{5}:{\\quad}\\frac{4πn+60+π}{10}$$", "input": "\\frac{\\frac{4πn+60+π}{2}}{5}", "result": "=-\\frac{4πn+π+60}{10}", "steps": [ { "type": "step", "primary": "Apply the fraction rule: $$\\frac{\\frac{b}{c}}{a}=\\frac{b}{c\\:\\cdot\\:a}$$", "result": "=\\frac{4πn+60+π}{2\\cdot\\:5}" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:5=10$$", "result": "=\\frac{4πn+60+π}{10}" } ], "meta": { "interimType": "Algebraic Manipulation Simplify Title 1Eq" } }, { "type": "step", "result": "=-\\frac{4πn+60+π}{10}" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7rWv8Qj96y2UCfi+p66aEe1gIkpdE5/64bYWapz6cM7dZFOWuRXr3JVDlRoxQBmIvHfGrQDRPH5zDTayBXmxDB2mrLkFle8FWLfuQyEISvpzNGoPE9TME3q+OPmgkv2RQ7oquj6i4tgpnYLqarsJ0mzWSdAsOj360xGHh5tgKGlejeh7+jKEzLb7VNCEMF3Z/bMzoTd+5nEXVeQoBhpFcIItzBkaB4G63Z3M0jm6w6pIPAyzzOHoQmsUtIXrXy0/YZxokaFbbtb0U7x2wO/zsmDCsio/RtQQ3RD3LfUwLffU3w/cRYUuMMCCSlLNtLuWN" } }, { "type": "step", "result": "x=-\\frac{4πn+60+π}{10}" } ], "meta": { "interimType": "Generic Simplify 0Eq" } } ], "meta": { "interimType": "Divide Both Sides Specific 1Eq", "gptData": "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" } }, { "type": "step", "result": "x=2πn+\\frac{π}{2}-70,\\:x=-\\frac{4πn+60+π}{10}" } ], "meta": { "solvingClass": "Equations", "interimType": "Equations" } }, { "type": "step", "result": "x=2πn+\\frac{π}{2}-70,\\:x=-\\frac{4πn+60+π}{10}" } ], "meta": { "solvingClass": "Trig Equations", "practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations", "practiceTopic": "Trig Equations" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "\\sin(2x-20)+\\cos(3x+50)" }, "showViewLarger": true } }, "meta": { "showVerify": true } }